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experimental-projects

(★ 10)

Highly experimental personal projects.

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# experimental-projects

Highly experimental personal projects.

### Summary

* [Aliquot-sequences](./aliquot-sequences)
    * [download elf files.sf](./aliquot-sequences/download_elf_files.sf)
    * [download graphs.sf](./aliquot-sequences/download_graphs.sf)
    * [elf2data.sf](./aliquot-sequences/elf2data.sf)
* [Can-you-find](./can-you-find)
    * [A repunit number which can be represented as difference of two squares in exactly three different ways](./can-you-find/A%20repunit%20number%20which%20can%20be%20represented%20as%20difference%20of%20two%20squares%20in%20exactly%20three%20different%20ways)
        * [prog.sf](./can-you-find/A%20repunit%20number%20which%20can%20be%20represented%20as%20difference%20of%20two%20squares%20in%20exactly%20three%20different%20ways/prog.sf)
    * [A triangular number other than 1, 10 and 10011 which contain the digit 0 and 1 only](./can-you-find/A%20triangular%20number%20other%20than%201,%2010%20and%2010011%20which%20contain%20the%20digit%200%20and%201%20only)
        * [prog.pl](./can-you-find/A%20triangular%20number%20other%20than%201,%2010%20and%2010011%20which%20contain%20the%20digit%200%20and%201%20only/prog.pl)
    * [Largest number n such that both n and the n-th triangular number has only odd digits](./can-you-find/Largest%20number%20n%20such%20that%20both%20n%20and%20the%20n-th%20triangular%20number%20has%20only%20odd%20digits)
        * [search.sf](./can-you-find/Largest%20number%20n%20such%20that%20both%20n%20and%20the%20n-th%20triangular%20number%20has%20only%20odd%20digits/search.sf)
* [Cgi-projects](./cgi-projects)
    * [Dark-search-engine](./cgi-projects/dark-search-engine)
        * [search.fcgi](./cgi-projects/dark-search-engine/search.fcgi)
        * [search berkeley.fcgi](./cgi-projects/dark-search-engine/search_berkeley.fcgi)
        * [search berkeley deep.fcgi](./cgi-projects/dark-search-engine/search_berkeley_deep.fcgi)
        * [Utils](./cgi-projects/dark-search-engine/utils)
            * [berkeley count entries.pl](./cgi-projects/dark-search-engine/utils/berkeley_count_entries.pl)
            * [content db to berkeley db.pl](./cgi-projects/dark-search-engine/utils/content_db_to_berkeley_db.pl)
            * [content db to berkeley db btree.pl](./cgi-projects/dark-search-engine/utils/content_db_to_berkeley_db_btree.pl)
            * [gdbm count entries.pl](./cgi-projects/dark-search-engine/utils/gdbm_count_entries.pl)
            * [gdbm to berkeley.pl](./cgi-projects/dark-search-engine/utils/gdbm_to_berkeley.pl)
            * [gdbm to berkeley btree.pl](./cgi-projects/dark-search-engine/utils/gdbm_to_berkeley_btree.pl)
            * [json2storable db.pl](./cgi-projects/dark-search-engine/utils/json2storable_db.pl)
            * [zstd db.pl](./cgi-projects/dark-search-engine/utils/zstd_db.pl)
    * [Filesystem-web-share](./cgi-projects/filesystem-web-share)
        * [index.cgi](./cgi-projects/filesystem-web-share/index.cgi)
        * [index.fcgi](./cgi-projects/filesystem-web-share/index.fcgi)
    * [Sidef-simple-web-interface](./cgi-projects/sidef-simple-web-interface)
        * [index.cgi](./cgi-projects/sidef-simple-web-interface/index.cgi)
        * [index.fcgi](./cgi-projects/sidef-simple-web-interface/index.fcgi)
    * [Sidef-web-interface](./cgi-projects/sidef-web-interface)
        * [index.cgi](./cgi-projects/sidef-web-interface/index.cgi)
        * [index.fcgi](./cgi-projects/sidef-web-interface/index.fcgi)
    * [Upload](./cgi-projects/upload)
        * [index.cgi](./cgi-projects/upload/index.cgi)
* [Cicada-3301](./cicada-3301)
    * [2012](./cicada-3301/2012)
        * [book-code part2.py](./cicada-3301/2012/book-code_part2.py)
        * [crypt-rsa-decrypt.pl](./cicada-3301/2012/crypt-rsa-decrypt.pl)
        * [decode binary file.sf](./cicada-3301/2012/decode_binary_file.sf)
        * [song-decode.py](./cicada-3301/2012/song-decode.py)
    * [book-code.py](./cicada-3301/book-code.py)
    * [crypt rsa.pl](./cicada-3301/crypt_rsa.pl)
    * [Extra](./cicada-3301/extra)
        * [crypt rsa sign.pl](./cicada-3301/extra/crypt_rsa_sign.pl)
        * [crypt rsa the game.pl](./cicada-3301/extra/crypt_rsa_the_game.pl)
    * [rune converter.py](./cicada-3301/rune_converter.py)
    * [Scripts](./cicada-3301/scripts)
        * [hash bruteforce blake.pl](./cicada-3301/scripts/hash_bruteforce_blake.pl)
        * [hash bruteforce sha512.pl](./cicada-3301/scripts/hash_bruteforce_sha512.pl)
    * [Tools](./cicada-3301/tools)
        * [and files.pl](./cicada-3301/tools/and_files.pl)
        * [binview.pl](./cicada-3301/tools/binview.pl)
        * [extract jpegs.pl](./cicada-3301/tools/extract_jpegs.pl)
        * [flip.pl](./cicada-3301/tools/flip.pl)
        * [freq.pl](./cicada-3301/tools/freq.pl)
        * [from hex.pl](./cicada-3301/tools/from_hex.pl)
        * [or files.pl](./cicada-3301/tools/or_files.pl)
        * [reverse.pl](./cicada-3301/tools/reverse.pl)
        * [visualize.pl](./cicada-3301/tools/visualize.pl)
        * [xor files.pl](./cicada-3301/tools/xor_files.pl)
* [Factordb](./factordb)
    * [auto.sf](./factordb/auto.sf)
    * [batch gcd factor.sf](./factordb/batch_gcd_factor.sf)
    * [batch gcd factor 2.sf](./factordb/batch_gcd_factor_2.sf)
    * [factordb.pl](./factordb/factordb.pl)
    * [factordb old.pl](./factordb/factordb_old.pl)
    * [factorize product of expressions.sf](./factordb/factorize_product_of_expressions.sf)
    * [generate fermat psp.sf](./factordb/generate_fermat_psp.sf)
    * [get factordb.pl](./factordb/get_factordb.pl)
    * [miller factor.sf](./factordb/miller_factor.sf)
    * [report factors.pl](./factordb/report_factors.pl)
    * [report factors 2.pl](./factordb/report_factors_2.pl)
    * [scrape factordb.pl](./factordb/scrape_factordb.pl)
    * [special factors.sf](./factordb/special_factors.sf)
* [Gnfs](./gnfs)
    * [C128](./gnfs/C128)
        * [factmsieve.py](./gnfs/C128/factmsieve.py)
    * [factmsieve.py](./gnfs/factmsieve.py)
* [Highly-composite-numbers](./highly-composite-numbers)
    * [hcn.pl](./highly-composite-numbers/hcn.pl)
    * [hcn between twin primes.pl](./highly-composite-numbers/hcn_between_twin_primes.pl)
    * [hcn divisible by 2^n.pl](./highly-composite-numbers/hcn_divisible_by_2^n.pl)
    * [hcn plus1 is square.pl](./highly-composite-numbers/hcn_plus1_is_square.pl)
    * [hcn plus minus 1 is prime.pl](./highly-composite-numbers/hcn_plus_minus_1_is_prime.pl)
    * [hcn product of 4 consecutive integers.pl](./highly-composite-numbers/hcn_product_of_4_consecutive_integers.pl)
    * [hcn smooth primes plus minus 1.pl](./highly-composite-numbers/hcn_smooth_primes_plus_minus_1.pl)
    * [Old](./highly-composite-numbers/Old)
        * [hcn.pl](./highly-composite-numbers/Old/hcn.pl)
        * [hcn between twin primes.pl](./highly-composite-numbers/Old/hcn_between_twin_primes.pl)
* [Oeis-drafts](./oeis-drafts)
    * [make it local.pl](./oeis-drafts/make_it_local.pl)
    * [oeis drafts.pl](./oeis-drafts/oeis_drafts.pl)
* [Oeis-research](./oeis-research)
    * [Ahmad J. Masad](./oeis-research/Ahmad%20J.%20Masad)
        * [Nearest integer to prime(n)^prime(n+1) ÷ prime(n+1)^prime(n)](./oeis-research/Ahmad%20J.%20Masad/Nearest%20integer%20to%20prime(n)^prime(n+1)%20÷%20prime(n+1)^prime(n))
            * [prog.pl](./oeis-research/Ahmad%20J.%20Masad/Nearest%20integer%20to%20prime(n)^prime(n+1)%20÷%20prime(n+1)^prime(n)/prog.pl)
    * [Albert Böschow](./oeis-research/Albert%20Böschow)
        * [Numbers k where phi(k) divides k - 3](./oeis-research/Albert%20Böschow/Numbers%20k%20where%20phi(k)%20divides%20k%20-%203)
            * [smooth search.pl](./oeis-research/Albert%20Böschow/Numbers%20k%20where%20phi(k)%20divides%20k%20-%203/smooth_search.pl)
    * [Alex Costea](./oeis-research/Alex%20Costea)
        * [Integers k divided by log2(k) are almost integers](./oeis-research/Alex%20Costea/Integers%20k%20divided%20by%20log2(k)%20are%20almost%20integers)
            * [binary search.sf](./oeis-research/Alex%20Costea/Integers%20k%20divided%20by%20log2(k)%20are%20almost%20integers/binary_search.sf)
            * [prog.pl](./oeis-research/Alex%20Costea/Integers%20k%20divided%20by%20log2(k)%20are%20almost%20integers/prog.pl)
    * [Alex Ratushnyak](./oeis-research/Alex%20Ratushnyak)
        * [Least k such that sum of (k over prime(k))^n first exceeds 1](./oeis-research/Alex%20Ratushnyak/Least%20k%20such%20that%20sum%20of%20(k%20over%20prime(k))^n%20first%20exceeds%201)
            * [prog.pl](./oeis-research/Alex%20Ratushnyak/Least%20k%20such%20that%20sum%20of%20(k%20over%20prime(k))^n%20first%20exceeds%201/prog.pl)
        * [Least positive k such that n*k^k - 1 is a prime](./oeis-research/Alex%20Ratushnyak/Least%20positive%20k%20such%20that%20n*k^k%20-%201%20is%20a%20prime)
            * [prog.sf](./oeis-research/Alex%20Ratushnyak/Least%20positive%20k%20such%20that%20n*k^k%20-%201%20is%20a%20prime/prog.sf)
            * [prog2.sf](./oeis-research/Alex%20Ratushnyak/Least%20positive%20k%20such%20that%20n*k^k%20-%201%20is%20a%20prime/prog2.sf)
        * [Numbers such that both their ternary and Zeckendorf representations are palindromic](./oeis-research/Alex%20Ratushnyak/Numbers%20such%20that%20both%20their%20ternary%20and%20Zeckendorf%20representations%20are%20palindromic)
            * [prog.pl](./oeis-research/Alex%20Ratushnyak/Numbers%20such%20that%20both%20their%20ternary%20and%20Zeckendorf%20representations%20are%20palindromic/prog.pl)
    * [Alexander Adamchuk](./oeis-research/Alexander%20Adamchuk)
        * [3-harmonic prime numerators](./oeis-research/Alexander%20Adamchuk/3-harmonic%20prime%20numerators)
            * [prog.sf](./oeis-research/Alexander%20Adamchuk/3-harmonic%20prime%20numerators/prog.sf)
        * [Largest prime divisor of Lucas(5*n)](./oeis-research/Alexander%20Adamchuk/Largest%20prime%20divisor%20of%20Lucas(5*n))
            * [prog.sf](./oeis-research/Alexander%20Adamchuk/Largest%20prime%20divisor%20of%20Lucas(5*n)/prog.sf)
        * [Largest prime factor of central factorial number](./oeis-research/Alexander%20Adamchuk/Largest%20prime%20factor%20of%20central%20factorial%20number)
            * [prog.sf](./oeis-research/Alexander%20Adamchuk/Largest%20prime%20factor%20of%20central%20factorial%20number/prog.sf)
        * [Prime numerator of sum of prime powers](./oeis-research/Alexander%20Adamchuk/Prime%20numerator%20of%20sum%20of%20prime%20powers)
            * [prog.sf](./oeis-research/Alexander%20Adamchuk/Prime%20numerator%20of%20sum%20of%20prime%20powers/prog.sf)
    * [Alexander R. Povolotsky](./oeis-research/Alexander%20R.%20Povolotsky)
        * [Indices of squares in A068869](./oeis-research/Alexander%20R.%20Povolotsky/Indices%20of%20squares%20in%20A068869)
            * [prog.pl](./oeis-research/Alexander%20R.%20Povolotsky/Indices%20of%20squares%20in%20A068869/prog.pl)
        * [No "n" exist, such that ( n! + prime(n) ) = m^k, where k>1](./oeis-research/Alexander%20R.%20Povolotsky/No%20"n"%20exist,%20such%20that%20(%20n!%20+%20prime(n)%20)%20=%20m^k,%20where%20k>1)
            * [prog.pl](./oeis-research/Alexander%20R.%20Povolotsky/No%20"n"%20exist,%20such%20that%20(%20n!%20+%20prime(n)%20)%20=%20m^k,%20where%20k>1/prog.pl)
    * [Altug Alkan](./oeis-research/Altug%20Alkan)
        * [A(n) is the smallest k such that psi(k) = factorial(n)](./oeis-research/Altug%20Alkan/a(n)%20is%20the%20smallest%20k%20such%20that%20psi(k)%20=%20factorial(n))
            * [prog.sf](./oeis-research/Altug%20Alkan/a(n)%20is%20the%20smallest%20k%20such%20that%20psi(k)%20=%20factorial(n)/prog.sf)
        * [A(n) is the smallest k such that usigma(k) = primorial(n)](./oeis-research/Altug%20Alkan/a(n)%20is%20the%20smallest%20k%20such%20that%20usigma(k)%20=%20primorial(n))
            * [prog.sf](./oeis-research/Altug%20Alkan/a(n)%20is%20the%20smallest%20k%20such%20that%20usigma(k)%20=%20primorial(n)/prog.sf)
            * [upper-bounds.sf](./oeis-research/Altug%20Alkan/a(n)%20is%20the%20smallest%20k%20such%20that%20usigma(k)%20=%20primorial(n)/upper-bounds.sf)
        * [Carmichael numbers n such that n-1 is a perfect power](./oeis-research/Altug%20Alkan/Carmichael%20numbers%20n%20such%20that%20n-1%20is%20a%20perfect%20power)
            * [prog.pl](./oeis-research/Altug%20Alkan/Carmichael%20numbers%20n%20such%20that%20n-1%20is%20a%20perfect%20power/prog.pl)
            * [smooth.pl](./oeis-research/Altug%20Alkan/Carmichael%20numbers%20n%20such%20that%20n-1%20is%20a%20perfect%20power/smooth.pl)
        * [Composite integers n such that the sum of the Pell numbers is divisible by n](./oeis-research/Altug%20Alkan/Composite%20integers%20n%20such%20that%20the%20sum%20of%20the%20Pell%20numbers%20is%20divisible%20by%20n)
            * [prog.pl](./oeis-research/Altug%20Alkan/Composite%20integers%20n%20such%20that%20the%20sum%20of%20the%20Pell%20numbers%20is%20divisible%20by%20n/prog.pl)
        * [Integers n such that n-th prime divides the n-th golden rectangle number](./oeis-research/Altug%20Alkan/Integers%20n%20such%20that%20n-th%20prime%20divides%20the%20n-th%20golden%20rectangle%20number)
            * [prog.pl](./oeis-research/Altug%20Alkan/Integers%20n%20such%20that%20n-th%20prime%20divides%20the%20n-th%20golden%20rectangle%20number/prog.pl)
        * [Integers n such that the n-th prime divides the n-th Pell number](./oeis-research/Altug%20Alkan/Integers%20n%20such%20that%20the%20n-th%20prime%20divides%20the%20n-th%20Pell%20number)
            * [prog.pl](./oeis-research/Altug%20Alkan/Integers%20n%20such%20that%20the%20n-th%20prime%20divides%20the%20n-th%20Pell%20number/prog.pl)
        * [Least k such that k is the product of n distinct primes and sigma(k) is an n-th power](./oeis-research/Altug%20Alkan/Least%20k%20such%20that%20k%20is%20the%20product%20of%20n%20distinct%20primes%20and%20sigma(k)%20is%20an%20n-th%20power)
            * [inverse sigma.pl](./oeis-research/Altug%20Alkan/Least%20k%20such%20that%20k%20is%20the%20product%20of%20n%20distinct%20primes%20and%20sigma(k)%20is%20an%20n-th%20power/inverse_sigma.pl)
            * [inverse sigma.sf](./oeis-research/Altug%20Alkan/Least%20k%20such%20that%20k%20is%20the%20product%20of%20n%20distinct%20primes%20and%20sigma(k)%20is%20an%20n-th%20power/inverse_sigma.sf)
            * [smooth generate.pl](./oeis-research/Altug%20Alkan/Least%20k%20such%20that%20k%20is%20the%20product%20of%20n%20distinct%20primes%20and%20sigma(k)%20is%20an%20n-th%20power/smooth_generate.pl)
            * [smooth generate almost primes.pl](./oeis-research/Altug%20Alkan/Least%20k%20such%20that%20k%20is%20the%20product%20of%20n%20distinct%20primes%20and%20sigma(k)%20is%20an%20n-th%20power/smooth_generate_almost_primes.pl)
            * [squarefree almost primes.pl](./oeis-research/Altug%20Alkan/Least%20k%20such%20that%20k%20is%20the%20product%20of%20n%20distinct%20primes%20and%20sigma(k)%20is%20an%20n-th%20power/squarefree_almost_primes.pl)
        * [Least k such that k^n + 1 is the product of n distinct primes](./oeis-research/Altug%20Alkan/Least%20k%20such%20that%20k^n%20+%201%20is%20the%20product%20of%20n%20distinct%20primes)
            * [is squarefree omega prime.sf](./oeis-research/Altug%20Alkan/Least%20k%20such%20that%20k^n%20+%201%20is%20the%20product%20of%20n%20distinct%20primes/is_squarefree_omega_prime.sf)
            * [prog.sf](./oeis-research/Altug%20Alkan/Least%20k%20such%20that%20k^n%20+%201%20is%20the%20product%20of%20n%20distinct%20primes/prog.sf)
        * [Least k such that phi(k) is an n-th power when k is the product of n distinct primes](./oeis-research/Altug%20Alkan/Least%20k%20such%20that%20phi(k)%20is%20an%20n-th%20power%20when%20k%20is%20the%20product%20of%20n%20distinct%20primes)
            * [generate squarefree almost primes.pl](./oeis-research/Altug%20Alkan/Least%20k%20such%20that%20phi(k)%20is%20an%20n-th%20power%20when%20k%20is%20the%20product%20of%20n%20distinct%20primes/generate_squarefree_almost_primes.pl)
            * [generate squarefree almost primes.sf](./oeis-research/Altug%20Alkan/Least%20k%20such%20that%20phi(k)%20is%20an%20n-th%20power%20when%20k%20is%20the%20product%20of%20n%20distinct%20primes/generate_squarefree_almost_primes.sf)
            * [generate squarefree almost primes 2.sf](./oeis-research/Altug%20Alkan/Least%20k%20such%20that%20phi(k)%20is%20an%20n-th%20power%20when%20k%20is%20the%20product%20of%20n%20distinct%20primes/generate_squarefree_almost_primes_2.sf)
            * [generate squarefree almost primes upper-bounds.pl](./oeis-research/Altug%20Alkan/Least%20k%20such%20that%20phi(k)%20is%20an%20n-th%20power%20when%20k%20is%20the%20product%20of%20n%20distinct%20primes/generate_squarefree_almost_primes_upper-bounds.pl)
            * [inverse phi.pl](./oeis-research/Altug%20Alkan/Least%20k%20such%20that%20phi(k)%20is%20an%20n-th%20power%20when%20k%20is%20the%20product%20of%20n%20distinct%20primes/inverse_phi.pl)
            * [smooth generate.pl](./oeis-research/Altug%20Alkan/Least%20k%20such%20that%20phi(k)%20is%20an%20n-th%20power%20when%20k%20is%20the%20product%20of%20n%20distinct%20primes/smooth_generate.pl)
            * [smooth generate almost primes.pl](./oeis-research/Altug%20Alkan/Least%20k%20such%20that%20phi(k)%20is%20an%20n-th%20power%20when%20k%20is%20the%20product%20of%20n%20distinct%20primes/smooth_generate_almost_primes.pl)
        * [Least k such that sigma(k) is a Fibonacci number when k is the product of n distinct primes](./oeis-research/Altug%20Alkan/Least%20k%20such%20that%20sigma(k)%20is%20a%20Fibonacci%20number%20when%20k%20is%20the%20product%20of%20n%20distinct%20primes)
            * [prog.sf](./oeis-research/Altug%20Alkan/Least%20k%20such%20that%20sigma(k)%20is%20a%20Fibonacci%20number%20when%20k%20is%20the%20product%20of%20n%20distinct%20primes/prog.sf)
        * [Least prime p such that p^n + 1 is the product of n distinct primes](./oeis-research/Altug%20Alkan/Least%20prime%20p%20such%20that%20p^n%20+%201%20is%20the%20product%20of%20n%20distinct%20primes)
            * [is squarefree omega prime.sf](./oeis-research/Altug%20Alkan/Least%20prime%20p%20such%20that%20p^n%20+%201%20is%20the%20product%20of%20n%20distinct%20primes/is_squarefree_omega_prime.sf)
            * [prog.pl](./oeis-research/Altug%20Alkan/Least%20prime%20p%20such%20that%20p^n%20+%201%20is%20the%20product%20of%20n%20distinct%20primes/prog.pl)
            * [prog.sf](./oeis-research/Altug%20Alkan/Least%20prime%20p%20such%20that%20p^n%20+%201%20is%20the%20product%20of%20n%20distinct%20primes/prog.sf)
        * [Smallest k such that psi(k) and phi(k) have same distinct prime factors when k is the product of n distinct primes](./oeis-research/Altug%20Alkan/Smallest%20k%20such%20that%20psi(k)%20and%20phi(k)%20have%20same%20distinct%20prime%20factors%20when%20k%20is%20the%20product%20of%20n%20distinct%20primes)
            * [generate squarefree almost primes.sf](./oeis-research/Altug%20Alkan/Smallest%20k%20such%20that%20psi(k)%20and%20phi(k)%20have%20same%20distinct%20prime%20factors%20when%20k%20is%20the%20product%20of%20n%20distinct%20primes/generate_squarefree_almost_primes.sf)
            * [simplified prog.sf](./oeis-research/Altug%20Alkan/Smallest%20k%20such%20that%20psi(k)%20and%20phi(k)%20have%20same%20distinct%20prime%20factors%20when%20k%20is%20the%20product%20of%20n%20distinct%20primes/simplified_prog.sf)
            * [smooth upper-bounds.pl](./oeis-research/Altug%20Alkan/Smallest%20k%20such%20that%20psi(k)%20and%20phi(k)%20have%20same%20distinct%20prime%20factors%20when%20k%20is%20the%20product%20of%20n%20distinct%20primes/smooth_upper-bounds.pl)
    * [Amarnath Murthy](./oeis-research/Amarnath%20Murthy)
        * [A(1) = 1, for n>1 a(n) = largest prime divisor of A062273(n)](./oeis-research/Amarnath%20Murthy/a(1)%20=%201,%20for%20n>1%20a(n)%20=%20largest%20prime%20divisor%20of%20A062273(n))
            * [prog.sf](./oeis-research/Amarnath%20Murthy/a(1)%20=%201,%20for%20n>1%20a(n)%20=%20largest%20prime%20divisor%20of%20A062273(n)/prog.sf)
        * [A(1) = 2, a(n+1) = a(n)-th squarefree number](./oeis-research/Amarnath%20Murthy/a(1)%20=%202,%20a(n+1)%20=%20a(n)-th%20squarefree%20number)
            * [prog.sf](./oeis-research/Amarnath%20Murthy/a(1)%20=%202,%20a(n+1)%20=%20a(n)-th%20squarefree%20number/prog.sf)
        * [A(n) = the largest prime divisor of the number C(n) formed from the concatenation of 1,2,3,... up to n](./oeis-research/Amarnath%20Murthy/a(n)%20=%20the%20largest%20prime%20divisor%20of%20the%20number%20C(n)%20formed%20from%20the%20concatenation%20of%201,2,3,...%20up%20to%20n)
            * [prog.sf](./oeis-research/Amarnath%20Murthy/a(n)%20=%20the%20largest%20prime%20divisor%20of%20the%20number%20C(n)%20formed%20from%20the%20concatenation%20of%201,2,3,...%20up%20to%20n/prog.sf)
        * [A(n) = the largest prime divisor of the number C(n) formed from the reverse concatenation of 1,2,3,... up to n](./oeis-research/Amarnath%20Murthy/a(n)%20=%20the%20largest%20prime%20divisor%20of%20the%20number%20C(n)%20formed%20from%20the%20reverse%20concatenation%20of%201,2,3,...%20up%20to%20n)
            * [prog.sf](./oeis-research/Amarnath%20Murthy/a(n)%20=%20the%20largest%20prime%20divisor%20of%20the%20number%20C(n)%20formed%20from%20the%20reverse%20concatenation%20of%201,2,3,...%20up%20to%20n/prog.sf)
        * [Least k such that k*prime(k) > 10^n](./oeis-research/Amarnath%20Murthy/Least%20k%20such%20that%20k*prime(k)%20>%2010^n)
            * [prog.pl](./oeis-research/Amarnath%20Murthy/Least%20k%20such%20that%20k*prime(k)%20>%2010^n/prog.pl)
        * [Smallest k such that n, k and n+k have the same prime signature](./oeis-research/Amarnath%20Murthy/Smallest%20k%20such%20that%20n,%20k%20and%20n+k%20have%20the%20same%20prime%20signature)
            * [chinese upper-bounds.pl](./oeis-research/Amarnath%20Murthy/Smallest%20k%20such%20that%20n,%20k%20and%20n+k%20have%20the%20same%20prime%20signature/chinese_upper-bounds.pl)
            * [chinese upper-bounds.sf](./oeis-research/Amarnath%20Murthy/Smallest%20k%20such%20that%20n,%20k%20and%20n+k%20have%20the%20same%20prime%20signature/chinese_upper-bounds.sf)
            * [chinese upper-bounds 2.pl](./oeis-research/Amarnath%20Murthy/Smallest%20k%20such%20that%20n,%20k%20and%20n+k%20have%20the%20same%20prime%20signature/chinese_upper-bounds_2.pl)
            * [chinese upper-bounds 2.sf](./oeis-research/Amarnath%20Murthy/Smallest%20k%20such%20that%20n,%20k%20and%20n+k%20have%20the%20same%20prime%20signature/chinese_upper-bounds_2.sf)
            * [prog.pl](./oeis-research/Amarnath%20Murthy/Smallest%20k%20such%20that%20n,%20k%20and%20n+k%20have%20the%20same%20prime%20signature/prog.pl)
            * [prog2.pl](./oeis-research/Amarnath%20Murthy/Smallest%20k%20such%20that%20n,%20k%20and%20n+k%20have%20the%20same%20prime%20signature/prog2.pl)
        * [Smallest number sandwiched between two numbers having exactly n prime divisors](./oeis-research/Amarnath%20Murthy/Smallest%20number%20sandwiched%20between%20two%20numbers%20having%20exactly%20n%20prime%20divisors)
            * [generate fast.pl](./oeis-research/Amarnath%20Murthy/Smallest%20number%20sandwiched%20between%20two%20numbers%20having%20exactly%20n%20prime%20divisors/generate_fast.pl)
            * [generate fast native.pl](./oeis-research/Amarnath%20Murthy/Smallest%20number%20sandwiched%20between%20two%20numbers%20having%20exactly%20n%20prime%20divisors/generate_fast_native.pl)
        * [Smallest prime p with bigomega(p-1)=n, where bigomega(m)=A001222(m) is the number of prime divisors of m (counted with multiplicity)](./oeis-research/Amarnath%20Murthy/Smallest%20prime%20p%20with%20bigomega(p-1)=n,%20where%20bigomega(m)=A001222(m)%20is%20the%20number%20of%20prime%20divisors%20of%20m%20(counted%20with%20multiplicity))
            * [prog.sf](./oeis-research/Amarnath%20Murthy/Smallest%20prime%20p%20with%20bigomega(p-1)=n,%20where%20bigomega(m)=A001222(m)%20is%20the%20number%20of%20prime%20divisors%20of%20m%20(counted%20with%20multiplicity)/prog.sf)
        * [Smallest prime which is 1 more than a product of n distinct primes: a(n) is a prime and a(n) - 1 is a squarefree number with n prime factors](./oeis-research/Amarnath%20Murthy/Smallest%20prime%20which%20is%201%20more%20than%20a%20product%20of%20n%20distinct%20primes:%20a(n)%20is%20a%20prime%20and%20a(n)%20-%201%20is%20a%20squarefree%20number%20with%20n%20prime%20factors)
            * [prog.pl](./oeis-research/Amarnath%20Murthy/Smallest%20prime%20which%20is%201%20more%20than%20a%20product%20of%20n%20distinct%20primes:%20a(n)%20is%20a%20prime%20and%20a(n)%20-%201%20is%20a%20squarefree%20number%20with%20n%20prime%20factors/prog.pl)
            * [prog.sf](./oeis-research/Amarnath%20Murthy/Smallest%20prime%20which%20is%201%20more%20than%20a%20product%20of%20n%20distinct%20primes:%20a(n)%20is%20a%20prime%20and%20a(n)%20-%201%20is%20a%20squarefree%20number%20with%20n%20prime%20factors/prog.sf)
        * [Sum of the remainders when n^2 is divided by squares < n](./oeis-research/Amarnath%20Murthy/Sum%20of%20the%20remainders%20when%20n^2%20is%20divided%20by%20squares%20<%20n)
            * [prog.sf](./oeis-research/Amarnath%20Murthy/Sum%20of%20the%20remainders%20when%20n^2%20is%20divided%20by%20squares%20<%20n/prog.sf)
    * [Amiram Eldar](./oeis-research/Amiram%20Eldar)
        * [A(n) is the least number k such that gpf(k)^n | k and gpf(k+1)^n | (k+1)](./oeis-research/Amiram%20Eldar/a(n)%20is%20the%20least%20number%20k%20such%20that%20gpf(k)^n%20|%20k%20and%20gpf(k+1)^n%20|%20(k+1))
            * [examples for a(4).pl](./oeis-research/Amiram%20Eldar/a(n)%20is%20the%20least%20number%20k%20such%20that%20gpf(k)^n%20|%20k%20and%20gpf(k+1)^n%20|%20(k+1)/examples_for_a(4).pl)
            * [prog.pl](./oeis-research/Amiram%20Eldar/a(n)%20is%20the%20least%20number%20k%20such%20that%20gpf(k)^n%20|%20k%20and%20gpf(k+1)^n%20|%20(k+1)/prog.pl)
            * [prog.sf](./oeis-research/Amiram%20Eldar/a(n)%20is%20the%20least%20number%20k%20such%20that%20gpf(k)^n%20|%20k%20and%20gpf(k+1)^n%20|%20(k+1)/prog.sf)
            * [search for a(5).pl](./oeis-research/Amiram%20Eldar/a(n)%20is%20the%20least%20number%20k%20such%20that%20gpf(k)^n%20|%20k%20and%20gpf(k+1)^n%20|%20(k+1)/search_for_a(5).pl)
        * [A(n) is the least number k such that the n-th odd squarefree divides lcm(1..k) over denom(harmonic(k))](./oeis-research/Amiram%20Eldar/a(n)%20is%20the%20least%20number%20k%20such%20that%20the%20n-th%20odd%20squarefree%20divides%20lcm(1..k)%20over%20denom(harmonic(k)))
            * [prog.sf](./oeis-research/Amiram%20Eldar/a(n)%20is%20the%20least%20number%20k%20such%20that%20the%20n-th%20odd%20squarefree%20divides%20lcm(1..k)%20over%20denom(harmonic(k))/prog.sf)
            * [search.pl](./oeis-research/Amiram%20Eldar/a(n)%20is%20the%20least%20number%20k%20such%20that%20the%20n-th%20odd%20squarefree%20divides%20lcm(1..k)%20over%20denom(harmonic(k))/search.pl)
        * [A(n) is the least start of exactly n consecutive numbers k that are sqrt(k)-smooth (A048098), or -1 in no such run exists](./oeis-research/Amiram%20Eldar/a(n)%20is%20the%20least%20start%20of%20exactly%20n%20consecutive%20numbers%20k%20that%20are%20sqrt(k)-smooth%20(A048098),%20or%20-1%20in%20no%20such%20run%20exists)
            * [prog.pl](./oeis-research/Amiram%20Eldar/a(n)%20is%20the%20least%20start%20of%20exactly%20n%20consecutive%20numbers%20k%20that%20are%20sqrt(k)-smooth%20(A048098),%20or%20-1%20in%20no%20such%20run%20exists/prog.pl)
        * [A(n) is the minimum number of distinct numbers with exactly n prime factors (counted with multiplicity) whose sum of reciprocals exceeds 1](./oeis-research/Amiram%20Eldar/a(n)%20is%20the%20minimum%20number%20of%20distinct%20numbers%20with%20exactly%20n%20prime%20factors%20(counted%20with%20multiplicity)%20whose%20sum%20of%20reciprocals%20exceeds%201)
            * [prog.pl](./oeis-research/Amiram%20Eldar/a(n)%20is%20the%20minimum%20number%20of%20distinct%20numbers%20with%20exactly%20n%20prime%20factors%20(counted%20with%20multiplicity)%20whose%20sum%20of%20reciprocals%20exceeds%201/prog.pl)
        * [Abundant Carmichael numbers](./oeis-research/Amiram%20Eldar/Abundant%20Carmichael%20numbers)
            * [comb.pl](./oeis-research/Amiram%20Eldar/Abundant%20Carmichael%20numbers/comb.pl)
            * [comb cyclic.pl](./oeis-research/Amiram%20Eldar/Abundant%20Carmichael%20numbers/comb_cyclic.pl)
            * [comb cyclic 2.pl](./oeis-research/Amiram%20Eldar/Abundant%20Carmichael%20numbers/comb_cyclic_2.pl)
            * [comb slow.sf](./oeis-research/Amiram%20Eldar/Abundant%20Carmichael%20numbers/comb_slow.sf)
            * [filter.pl](./oeis-research/Amiram%20Eldar/Abundant%20Carmichael%20numbers/filter.pl)
            * [from lcm.pl](./oeis-research/Amiram%20Eldar/Abundant%20Carmichael%20numbers/from_lcm.pl)
            * [from product.pl](./oeis-research/Amiram%20Eldar/Abundant%20Carmichael%20numbers/from_product.pl)
            * [gen.pl](./oeis-research/Amiram%20Eldar/Abundant%20Carmichael%20numbers/gen.pl)
            * [idea to try.sf](./oeis-research/Amiram%20Eldar/Abundant%20Carmichael%20numbers/idea_to_try.sf)
            * [l.sf](./oeis-research/Amiram%20Eldar/Abundant%20Carmichael%20numbers/l.sf)
            * [lcm.sf](./oeis-research/Amiram%20Eldar/Abundant%20Carmichael%20numbers/lcm.sf)
            * [new idea.sf](./oeis-research/Amiram%20Eldar/Abundant%20Carmichael%20numbers/new_idea.sf)
            * [new idea 2.sf](./oeis-research/Amiram%20Eldar/Abundant%20Carmichael%20numbers/new_idea_2.sf)
            * [new idea 3.sf](./oeis-research/Amiram%20Eldar/Abundant%20Carmichael%20numbers/new_idea_3.sf)
            * [new idea 4.sf](./oeis-research/Amiram%20Eldar/Abundant%20Carmichael%20numbers/new_idea_4.sf)
            * [w.pl](./oeis-research/Amiram%20Eldar/Abundant%20Carmichael%20numbers/w.pl)
            * [y.pl](./oeis-research/Amiram%20Eldar/Abundant%20Carmichael%20numbers/y.pl)
            * [z.pl](./oeis-research/Amiram%20Eldar/Abundant%20Carmichael%20numbers/z.pl)
        * [Bi-unitary divisors sum constant](./oeis-research/Amiram%20Eldar/bi-unitary%20divisors%20sum%20constant)
            * [prog.pl](./oeis-research/Amiram%20Eldar/bi-unitary%20divisors%20sum%20constant/prog.pl)
        * [Chernick-Carmichael number n prime factors](./oeis-research/Amiram%20Eldar/Chernick-Carmichael%20number%20n%20prime%20factors)
            * [Experiments](./oeis-research/Amiram%20Eldar/Chernick-Carmichael%20number%20n%20prime%20factors/experiments)
                * [prog.pl](./oeis-research/Amiram%20Eldar/Chernick-Carmichael%20number%20n%20prime%20factors/experiments/prog.pl)
            * [Lucas-Carmichael](./oeis-research/Amiram%20Eldar/Chernick-Carmichael%20number%20n%20prime%20factors/Lucas-Carmichael)
                * [find.pl](./oeis-research/Amiram%20Eldar/Chernick-Carmichael%20number%20n%20prime%20factors/Lucas-Carmichael/find.pl)
                * [modulo.sf](./oeis-research/Amiram%20Eldar/Chernick-Carmichael%20number%20n%20prime%20factors/Lucas-Carmichael/modulo.sf)
                * [prog.sf](./oeis-research/Amiram%20Eldar/Chernick-Carmichael%20number%20n%20prime%20factors/Lucas-Carmichael/prog.sf)
            * [Search for a(10)](./oeis-research/Amiram%20Eldar/Chernick-Carmichael%20number%20n%20prime%20factors/search%20for%20a(10))
                * [orig.pl](./oeis-research/Amiram%20Eldar/Chernick-Carmichael%20number%20n%20prime%20factors/search%20for%20a(10)/orig.pl)
                * [prog.pl](./oeis-research/Amiram%20Eldar/Chernick-Carmichael%20number%20n%20prime%20factors/search%20for%20a(10)/prog.pl)
            * [Search for a(12)](./oeis-research/Amiram%20Eldar/Chernick-Carmichael%20number%20n%20prime%20factors/search%20for%20a(12))
                * [a.pl](./oeis-research/Amiram%20Eldar/Chernick-Carmichael%20number%20n%20prime%20factors/search%20for%20a(12)/a.pl)
                * [bench.cpp](./oeis-research/Amiram%20Eldar/Chernick-Carmichael%20number%20n%20prime%20factors/search%20for%20a(12)/bench.cpp)
                * [Extra](./oeis-research/Amiram%20Eldar/Chernick-Carmichael%20number%20n%20prime%20factors/search%20for%20a(12)/Extra)
                    * [find a12.cpp](./oeis-research/Amiram%20Eldar/Chernick-Carmichael%20number%20n%20prime%20factors/search%20for%20a(12)/Extra/find_a12.cpp)
                    * [julia find a12.jl](./oeis-research/Amiram%20Eldar/Chernick-Carmichael%20number%20n%20prime%20factors/search%20for%20a(12)/Extra/julia_find_a12.jl)
                * [Julia](./oeis-research/Amiram%20Eldar/Chernick-Carmichael%20number%20n%20prime%20factors/search%20for%20a(12)/Julia)
                    * [a3-a10.jl](./oeis-research/Amiram%20Eldar/Chernick-Carmichael%20number%20n%20prime%20factors/search%20for%20a(12)/Julia/a3-a10.jl)
                * [new sieve.jl](./oeis-research/Amiram%20Eldar/Chernick-Carmichael%20number%20n%20prime%20factors/search%20for%20a(12)/new_sieve.jl)
                * [new sieve.pl](./oeis-research/Amiram%20Eldar/Chernick-Carmichael%20number%20n%20prime%20factors/search%20for%20a(12)/new_sieve.pl)
                * [r with 128.cpp](./oeis-research/Amiram%20Eldar/Chernick-Carmichael%20number%20n%20prime%20factors/search%20for%20a(12)/r_with_128.cpp)
                * [search a12.cpp](./oeis-research/Amiram%20Eldar/Chernick-Carmichael%20number%20n%20prime%20factors/search%20for%20a(12)/search_a12.cpp)
                * [search a12 v2.cpp](./oeis-research/Amiram%20Eldar/Chernick-Carmichael%20number%20n%20prime%20factors/search%20for%20a(12)/search_a12_v2.cpp)
                * [verify.sf](./oeis-research/Amiram%20Eldar/Chernick-Carmichael%20number%20n%20prime%20factors/search%20for%20a(12)/verify.sf)
                * [verify output.sf](./oeis-research/Amiram%20Eldar/Chernick-Carmichael%20number%20n%20prime%20factors/search%20for%20a(12)/verify_output.sf)
                * [x.cpp](./oeis-research/Amiram%20Eldar/Chernick-Carmichael%20number%20n%20prime%20factors/search%20for%20a(12)/x.cpp)
        * [Colltaz with sqrt(3) or 3](./oeis-research/Amiram%20Eldar/Colltaz%20with%20sqrt(3)%20or%203)
            * [prog.pl](./oeis-research/Amiram%20Eldar/Colltaz%20with%20sqrt(3)%20or%203/prog.pl)
            * [prog2.pl](./oeis-research/Amiram%20Eldar/Colltaz%20with%20sqrt(3)%20or%203/prog2.pl)
            * [u.sf](./oeis-research/Amiram%20Eldar/Colltaz%20with%20sqrt(3)%20or%203/u.sf)
        * [Composite numbers (pseudoprimes) n, that are not Carmichael numbers, such that A000670(n) == 1 (mod n)](./oeis-research/Amiram%20Eldar/Composite%20numbers%20(pseudoprimes)%20n,%20that%20are%20not%20Carmichael%20numbers,%20such%20that%20A000670(n)%20==%201%20(mod%20n))
            * [prog.pl](./oeis-research/Amiram%20Eldar/Composite%20numbers%20(pseudoprimes)%20n,%20that%20are%20not%20Carmichael%20numbers,%20such%20that%20A000670(n)%20==%201%20(mod%20n)/prog.pl)
            * [prog faster.pl](./oeis-research/Amiram%20Eldar/Composite%20numbers%20(pseudoprimes)%20n,%20that%20are%20not%20Carmichael%20numbers,%20such%20that%20A000670(n)%20==%201%20(mod%20n)/prog_faster.pl)
        * [Consecutive numbers whose sum of divisors has the same set of distinct prime divisors](./oeis-research/Amiram%20Eldar/Consecutive%20numbers%20whose%20sum%20of%20divisors%20has%20the%20same%20set%20of%20distinct%20prime%20divisors)
            * [prog.pl](./oeis-research/Amiram%20Eldar/Consecutive%20numbers%20whose%20sum%20of%20divisors%20has%20the%20same%20set%20of%20distinct%20prime%20divisors/prog.pl)
        * [Least k > 1 such that sigma(k) * phi(k) is an n-th perfect power](./oeis-research/Amiram%20Eldar/Least%20k%20>%201%20such%20that%20sigma(k)%20*%20phi(k)%20is%20an%20n-th%20perfect%20power)
            * [prog.pl](./oeis-research/Amiram%20Eldar/Least%20k%20>%201%20such%20that%20sigma(k)%20*%20phi(k)%20is%20an%20n-th%20perfect%20power/prog.pl)
            * [prog2 max power.pl](./oeis-research/Amiram%20Eldar/Least%20k%20>%201%20such%20that%20sigma(k)%20*%20phi(k)%20is%20an%20n-th%20perfect%20power/prog2_max_power.pl)
        * [Least number k such that A046660(k) = A046660(k+1) = n](./oeis-research/Amiram%20Eldar/Least%20number%20k%20such%20that%20A046660(k)%20=%20A046660(k+1)%20=%20n)
            * [upper-bounds.sf](./oeis-research/Amiram%20Eldar/Least%20number%20k%20such%20that%20A046660(k)%20=%20A046660(k+1)%20=%20n/upper-bounds.sf)
            * [upper-bounds with multiplier.sf](./oeis-research/Amiram%20Eldar/Least%20number%20k%20such%20that%20A046660(k)%20=%20A046660(k+1)%20=%20n/upper-bounds_with_multiplier.sf)
        * [Least number k such that A048105(k) = A048105(k+1) = 2*n, and 0 if it does not exist](./oeis-research/Amiram%20Eldar/Least%20number%20k%20such%20that%20A048105(k)%20=%20A048105(k+1)%20=%202*n,%20and%200%20if%20it%20does%20not%20exist)
            * [prog.pl](./oeis-research/Amiram%20Eldar/Least%20number%20k%20such%20that%20A048105(k)%20=%20A048105(k+1)%20=%202*n,%20and%200%20if%20it%20does%20not%20exist/prog.pl)
            * [smooth.pl](./oeis-research/Amiram%20Eldar/Least%20number%20k%20such%20that%20A048105(k)%20=%20A048105(k+1)%20=%202*n,%20and%200%20if%20it%20does%20not%20exist/smooth.pl)
            * [sort.sf](./oeis-research/Amiram%20Eldar/Least%20number%20k%20such%20that%20A048105(k)%20=%20A048105(k+1)%20=%202*n,%20and%200%20if%20it%20does%20not%20exist/sort.sf)
        * [Least number k such that there are exactly n cubefull numbers between k^3 and (k+1)^3](./oeis-research/Amiram%20Eldar/Least%20number%20k%20such%20that%20there%20are%20exactly%20n%20cubefull%20numbers%20between%20k^3%20and%20(k+1)^3)
            * [prog.sf](./oeis-research/Amiram%20Eldar/Least%20number%20k%20such%20that%20there%20are%20exactly%20n%20cubefull%20numbers%20between%20k^3%20and%20(k+1)^3/prog.sf)
        * [Least start of a run of exactly n successive powerful numbers that are pairwise coprime](./oeis-research/Amiram%20Eldar/Least%20start%20of%20a%20run%20of%20exactly%20n%20successive%20powerful%20numbers%20that%20are%20pairwise%20coprime)
            * [generate.pl](./oeis-research/Amiram%20Eldar/Least%20start%20of%20a%20run%20of%20exactly%20n%20successive%20powerful%20numbers%20that%20are%20pairwise%20coprime/generate.pl)
        * [Least super-Poulet number with n distinct prime factors](./oeis-research/Amiram%20Eldar/Least%20super-Poulet%20number%20with%20n%20distinct%20prime%20factors)
            * [extract primes.pl](./oeis-research/Amiram%20Eldar/Least%20super-Poulet%20number%20with%20n%20distinct%20prime%20factors/extract_primes.pl)
            * [generate from primes.pl](./oeis-research/Amiram%20Eldar/Least%20super-Poulet%20number%20with%20n%20distinct%20prime%20factors/generate_from_primes.pl)
            * [sort.pl](./oeis-research/Amiram%20Eldar/Least%20super-Poulet%20number%20with%20n%20distinct%20prime%20factors/sort.pl)
            * [super poulet pseudoprimes.pl](./oeis-research/Amiram%20Eldar/Least%20super-Poulet%20number%20with%20n%20distinct%20prime%20factors/super_poulet_pseudoprimes.pl)
            * [upper-bounds.pl](./oeis-research/Amiram%20Eldar/Least%20super-Poulet%20number%20with%20n%20distinct%20prime%20factors/upper-bounds.pl)
        * [Let k be the n-th perfect number, a(n) is the least number m such that k*d*m + 1 is prime for all of the proper divisors d of k so their product is a Carmichael number](./oeis-research/Amiram%20Eldar/Let%20k%20be%20the%20n-th%20perfect%20number,%20a(n)%20is%20the%20least%20number%20m%20such%20that%20k*d*m%20+%201%20is%20prime%20for%20all%20of%20the%20proper%20divisors%20d%20of%20k%20so%20their%20product%20is%20a%20Carmichael%20number)
            * [carmichael sieve.jl](./oeis-research/Amiram%20Eldar/Let%20k%20be%20the%20n-th%20perfect%20number,%20a(n)%20is%20the%20least%20number%20m%20such%20that%20k*d*m%20+%201%20is%20prime%20for%20all%20of%20the%20proper%20divisors%20d%20of%20k%20so%20their%20product%20is%20a%20Carmichael%20number/carmichael_sieve.jl)
            * [carmichael sieve.pl](./oeis-research/Amiram%20Eldar/Let%20k%20be%20the%20n-th%20perfect%20number,%20a(n)%20is%20the%20least%20number%20m%20such%20that%20k*d*m%20+%201%20is%20prime%20for%20all%20of%20the%20proper%20divisors%20d%20of%20k%20so%20their%20product%20is%20a%20Carmichael%20number/carmichael_sieve.pl)
            * [carmichael sieve a5.pl](./oeis-research/Amiram%20Eldar/Let%20k%20be%20the%20n-th%20perfect%20number,%20a(n)%20is%20the%20least%20number%20m%20such%20that%20k*d*m%20+%201%20is%20prime%20for%20all%20of%20the%20proper%20divisors%20d%20of%20k%20so%20their%20product%20is%20a%20Carmichael%20number/carmichael_sieve_a5.pl)
            * [find almost terms.sf](./oeis-research/Amiram%20Eldar/Let%20k%20be%20the%20n-th%20perfect%20number,%20a(n)%20is%20the%20least%20number%20m%20such%20that%20k*d*m%20+%201%20is%20prime%20for%20all%20of%20the%20proper%20divisors%20d%20of%20k%20so%20their%20product%20is%20a%20Carmichael%20number/find_almost_terms.sf)
            * [gen.pl](./oeis-research/Amiram%20Eldar/Let%20k%20be%20the%20n-th%20perfect%20number,%20a(n)%20is%20the%20least%20number%20m%20such%20that%20k*d*m%20+%201%20is%20prime%20for%20all%20of%20the%20proper%20divisors%20d%20of%20k%20so%20their%20product%20is%20a%20Carmichael%20number/gen.pl)
            * [lucas-carm-a4.cpp](./oeis-research/Amiram%20Eldar/Let%20k%20be%20the%20n-th%20perfect%20number,%20a(n)%20is%20the%20least%20number%20m%20such%20that%20k*d*m%20+%201%20is%20prime%20for%20all%20of%20the%20proper%20divisors%20d%20of%20k%20so%20their%20product%20is%20a%20Carmichael%20number/lucas-carm-a4.cpp)
            * [lucas-carmichael sieve.jl](./oeis-research/Amiram%20Eldar/Let%20k%20be%20the%20n-th%20perfect%20number,%20a(n)%20is%20the%20least%20number%20m%20such%20that%20k*d*m%20+%201%20is%20prime%20for%20all%20of%20the%20proper%20divisors%20d%20of%20k%20so%20their%20product%20is%20a%20Carmichael%20number/lucas-carmichael_sieve.jl)
            * [lucas-carmichael sieve.pl](./oeis-research/Amiram%20Eldar/Let%20k%20be%20the%20n-th%20perfect%20number,%20a(n)%20is%20the%20least%20number%20m%20such%20that%20k*d*m%20+%201%20is%20prime%20for%20all%20of%20the%20proper%20divisors%20d%20of%20k%20so%20their%20product%20is%20a%20Carmichael%20number/lucas-carmichael_sieve.pl)
            * [lucas-carmichael sieve a4.jl](./oeis-research/Amiram%20Eldar/Let%20k%20be%20the%20n-th%20perfect%20number,%20a(n)%20is%20the%20least%20number%20m%20such%20that%20k*d*m%20+%201%20is%20prime%20for%20all%20of%20the%20proper%20divisors%20d%20of%20k%20so%20their%20product%20is%20a%20Carmichael%20number/lucas-carmichael_sieve_a4.jl)
            * [lucas-carmichael sieve a4.pl](./oeis-research/Amiram%20Eldar/Let%20k%20be%20the%20n-th%20perfect%20number,%20a(n)%20is%20the%20least%20number%20m%20such%20that%20k*d*m%20+%201%20is%20prime%20for%20all%20of%20the%20proper%20divisors%20d%20of%20k%20so%20their%20product%20is%20a%20Carmichael%20number/lucas-carmichael_sieve_a4.pl)
        * [Lexicographically earliest sequence of numbers whose partial products are all Fermat pseudoprimes to base 2](./oeis-research/Amiram%20Eldar/Lexicographically%20earliest%20sequence%20of%20numbers%20whose%20partial%20products%20are%20all%20Fermat%20pseudoprimes%20to%20base%202)
            * [generate.pl](./oeis-research/Amiram%20Eldar/Lexicographically%20earliest%20sequence%20of%20numbers%20whose%20partial%20products%20are%20all%20Fermat%20pseudoprimes%20to%20base%202/generate.pl)
        * [Lexicographically earliest sequence of prime numbers whose partial products, starting from the second, are all Fermat pseudoprimes to base 2](./oeis-research/Amiram%20Eldar/Lexicographically%20earliest%20sequence%20of%20prime%20numbers%20whose%20partial%20products,%20starting%20from%20the%20second,%20are%20all%20Fermat%20pseudoprimes%20to%20base%202)
            * [generate.pl](./oeis-research/Amiram%20Eldar/Lexicographically%20earliest%20sequence%20of%20prime%20numbers%20whose%20partial%20products,%20starting%20from%20the%20second,%20are%20all%20Fermat%20pseudoprimes%20to%20base%202/generate.pl)
        * [Lexicographically earliest strictly increasing sequence of prime numbers whose partial products, starting from the second, are all Fermat pseudoprimes to base 2](./oeis-research/Amiram%20Eldar/Lexicographically%20earliest%20strictly%20increasing%20sequence%20of%20prime%20numbers%20whose%20partial%20products,%20starting%20from%20the%20second,%20are%20all%20Fermat%20pseudoprimes%20to%20base%202)
            * [generate.pl](./oeis-research/Amiram%20Eldar/Lexicographically%20earliest%20strictly%20increasing%20sequence%20of%20prime%20numbers%20whose%20partial%20products,%20starting%20from%20the%20second,%20are%20all%20Fermat%20pseudoprimes%20to%20base%202/generate.pl)
        * [Number of abundant numbers < 10^n](./oeis-research/Amiram%20Eldar/Number%20of%20abundant%20numbers%20<%2010^n)
            * [prog.pl](./oeis-research/Amiram%20Eldar/Number%20of%20abundant%20numbers%20<%2010^n/prog.pl)
        * [Number of primitive abundant numbers (A071395) < 10^n](./oeis-research/Amiram%20Eldar/Number%20of%20primitive%20abundant%20numbers%20(A071395)%20<%2010^n)
            * [generate.sf](./oeis-research/Amiram%20Eldar/Number%20of%20primitive%20abundant%20numbers%20(A071395)%20<%2010^n/generate.sf)
            * [prog.jl](./oeis-research/Amiram%20Eldar/Number%20of%20primitive%20abundant%20numbers%20(A071395)%20<%2010^n/prog.jl)
            * [prog.pl](./oeis-research/Amiram%20Eldar/Number%20of%20primitive%20abundant%20numbers%20(A071395)%20<%2010^n/prog.pl)
        * [Numbers k such that A168512(2^k) is a prime number](./oeis-research/Amiram%20Eldar/Numbers%20k%20such%20that%20A168512(2^k)%20is%20a%20prime%20number)
            * [search.pl](./oeis-research/Amiram%20Eldar/Numbers%20k%20such%20that%20A168512(2^k)%20is%20a%20prime%20number/search.pl)
        * [Numbers k such that F(k), F(k+1) and F(k+2) have the same binary weight (A000120), where F(k) is the k-th Fibonacci number (A000045)](./oeis-research/Amiram%20Eldar/Numbers%20k%20such%20that%20F(k),%20F(k+1)%20and%20F(k+2)%20have%20the%20same%20binary%20weight%20(A000120),%20where%20F(k)%20is%20the%20k-th%20Fibonacci%20number%20(A000045))
            * [prog.pl](./oeis-research/Amiram%20Eldar/Numbers%20k%20such%20that%20F(k),%20F(k+1)%20and%20F(k+2)%20have%20the%20same%20binary%20weight%20(A000120),%20where%20F(k)%20is%20the%20k-th%20Fibonacci%20number%20(A000045)/prog.pl)
        * [Numbers k such that gpf(k)^2 | k and gpf(k+1)^3 | (k+1)](./oeis-research/Amiram%20Eldar/Numbers%20k%20such%20that%20gpf(k)^2%20|%20k%20and%20gpf(k+1)^3%20|%20(k+1))
            * [prog.pl](./oeis-research/Amiram%20Eldar/Numbers%20k%20such%20that%20gpf(k)^2%20|%20k%20and%20gpf(k+1)^3%20|%20(k+1)/prog.pl)
            * [verify.sf](./oeis-research/Amiram%20Eldar/Numbers%20k%20such%20that%20gpf(k)^2%20|%20k%20and%20gpf(k+1)^3%20|%20(k+1)/verify.sf)
        * [Numbers k such that gpf(k)^2 | k and gpf(k+1)^4 | (k+1)](./oeis-research/Amiram%20Eldar/Numbers%20k%20such%20that%20gpf(k)^2%20|%20k%20and%20gpf(k+1)^4%20|%20(k+1))
            * [prog.pl](./oeis-research/Amiram%20Eldar/Numbers%20k%20such%20that%20gpf(k)^2%20|%20k%20and%20gpf(k+1)^4%20|%20(k+1)/prog.pl)
            * [verify.sf](./oeis-research/Amiram%20Eldar/Numbers%20k%20such%20that%20gpf(k)^2%20|%20k%20and%20gpf(k+1)^4%20|%20(k+1)/verify.sf)
        * [Numbers k such that gpf(k)^3 | k and gpf(k+1)^2 | (k+1)](./oeis-research/Amiram%20Eldar/Numbers%20k%20such%20that%20gpf(k)^3%20|%20k%20and%20gpf(k+1)^2%20|%20(k+1))
            * [prog.pl](./oeis-research/Amiram%20Eldar/Numbers%20k%20such%20that%20gpf(k)^3%20|%20k%20and%20gpf(k+1)^2%20|%20(k+1)/prog.pl)
            * [verify.sf](./oeis-research/Amiram%20Eldar/Numbers%20k%20such%20that%20gpf(k)^3%20|%20k%20and%20gpf(k+1)^2%20|%20(k+1)/verify.sf)
        * [Numbers k such that gpf(k)^4 | k and gpf(k+1)^2 | (k+1)](./oeis-research/Amiram%20Eldar/Numbers%20k%20such%20that%20gpf(k)^4%20|%20k%20and%20gpf(k+1)^2%20|%20(k+1))
            * [prog.pl](./oeis-research/Amiram%20Eldar/Numbers%20k%20such%20that%20gpf(k)^4%20|%20k%20and%20gpf(k+1)^2%20|%20(k+1)/prog.pl)
            * [prog.sf](./oeis-research/Amiram%20Eldar/Numbers%20k%20such%20that%20gpf(k)^4%20|%20k%20and%20gpf(k+1)^2%20|%20(k+1)/prog.sf)
            * [prog faster.sf](./oeis-research/Amiram%20Eldar/Numbers%20k%20such%20that%20gpf(k)^4%20|%20k%20and%20gpf(k+1)^2%20|%20(k+1)/prog_faster.sf)
            * [verify.sf](./oeis-research/Amiram%20Eldar/Numbers%20k%20such%20that%20gpf(k)^4%20|%20k%20and%20gpf(k+1)^2%20|%20(k+1)/verify.sf)
        * [Numbers k such that k and k+1 are both divisible by the cube of their largest prime factor](./oeis-research/Amiram%20Eldar/Numbers%20k%20such%20that%20k%20and%20k+1%20are%20both%20divisible%20by%20the%20cube%20of%20their%20largest%20prime%20factor)
            * [prog.pl](./oeis-research/Amiram%20Eldar/Numbers%20k%20such%20that%20k%20and%20k+1%20are%20both%20divisible%20by%20the%20cube%20of%20their%20largest%20prime%20factor/prog.pl)
        * [Numbers k such that the arithmetic mean of the first k squarefree numbers is an integer](./oeis-research/Amiram%20Eldar/Numbers%20k%20such%20that%20the%20arithmetic%20mean%20of%20the%20first%20k%20squarefree%20numbers%20is%20an%20integer)
            * [prog.pl](./oeis-research/Amiram%20Eldar/Numbers%20k%20such%20that%20the%20arithmetic%20mean%20of%20the%20first%20k%20squarefree%20numbers%20is%20an%20integer/prog.pl)
        * [Numbers m such that sigma(m) is a Lucas number](./oeis-research/Amiram%20Eldar/Numbers%20m%20such%20that%20sigma(m)%20is%20a%20Lucas%20number)
            * [prog.sf](./oeis-research/Amiram%20Eldar/Numbers%20m%20such%20that%20sigma(m)%20is%20a%20Lucas%20number/prog.sf)
        * [Numbers n such that n = pi(n) + uphi(n)](./oeis-research/Amiram%20Eldar/Numbers%20n%20such%20that%20n%20=%20pi(n)%20+%20uphi(n))
            * [prog.pl](./oeis-research/Amiram%20Eldar/Numbers%20n%20such%20that%20n%20=%20pi(n)%20+%20uphi(n)/prog.pl)
        * [Numbers n such that sigma(n) and sigma(n)-n are both triangular numbers](./oeis-research/Amiram%20Eldar/Numbers%20n%20such%20that%20sigma(n)%20and%20sigma(n)-n%20are%20both%20triangular%20numbers)
            * [prog.sf](./oeis-research/Amiram%20Eldar/Numbers%20n%20such%20that%20sigma(n)%20and%20sigma(n)-n%20are%20both%20triangular%20numbers/prog.sf)
        * [Numbers that are both infinitary and noninfinitary harmonic numbers](./oeis-research/Amiram%20Eldar/Numbers%20that%20are%20both%20infinitary%20and%20noninfinitary%20harmonic%20numbers)
            * [prog.sf](./oeis-research/Amiram%20Eldar/Numbers%20that%20are%20both%20infinitary%20and%20noninfinitary%20harmonic%20numbers/prog.sf)
            * [smooth search.pl](./oeis-research/Amiram%20Eldar/Numbers%20that%20are%20both%20infinitary%20and%20noninfinitary%20harmonic%20numbers/smooth_search.pl)
        * [Numbers that are both unitary and nonunitary harmonic numbers](./oeis-research/Amiram%20Eldar/Numbers%20that%20are%20both%20unitary%20and%20nonunitary%20harmonic%20numbers)
            * [prog.sf](./oeis-research/Amiram%20Eldar/Numbers%20that%20are%20both%20unitary%20and%20nonunitary%20harmonic%20numbers/prog.sf)
            * [smooth search.pl](./oeis-research/Amiram%20Eldar/Numbers%20that%20are%20both%20unitary%20and%20nonunitary%20harmonic%20numbers/smooth_search.pl)
        * [Numbers that are not powers of primes whose harmonic mean of their proper unitary divisors is an integer](./oeis-research/Amiram%20Eldar/Numbers%20that%20are%20not%20powers%20of%20primes%20whose%20harmonic%20mean%20of%20their%20proper%20unitary%20divisors%20is%20an%20integer)
            * [search.pl](./oeis-research/Amiram%20Eldar/Numbers%20that%20are%20not%20powers%20of%20primes%20whose%20harmonic%20mean%20of%20their%20proper%20unitary%20divisors%20is%20an%20integer/search.pl)
            * [search.sf](./oeis-research/Amiram%20Eldar/Numbers%20that%20are%20not%20powers%20of%20primes%20whose%20harmonic%20mean%20of%20their%20proper%20unitary%20divisors%20is%20an%20integer/search.sf)
            * [search inverse usigma.pl](./oeis-research/Amiram%20Eldar/Numbers%20that%20are%20not%20powers%20of%20primes%20whose%20harmonic%20mean%20of%20their%20proper%20unitary%20divisors%20is%20an%20integer/search_inverse_usigma.pl)
            * [smooth generate.pl](./oeis-research/Amiram%20Eldar/Numbers%20that%20are%20not%20powers%20of%20primes%20whose%20harmonic%20mean%20of%20their%20proper%20unitary%20divisors%20is%20an%20integer/smooth_generate.pl)
            * [x.pl](./oeis-research/Amiram%20Eldar/Numbers%20that%20are%20not%20powers%20of%20primes%20whose%20harmonic%20mean%20of%20their%20proper%20unitary%20divisors%20is%20an%20integer/x.pl)
        * [Odd numbers that are not safe primes such that p-1 | k-1 or k-1 | p-1 for every prime p | 2^(k-1)-1](./oeis-research/Amiram%20Eldar/Odd%20numbers%20that%20are%20not%20safe%20primes%20such%20that%20p-1%20|%20k-1%20or%20k-1%20|%20p-1%20for%20every%20prime%20p%20|%202^(k-1)-1)
            * [prog.sf](./oeis-research/Amiram%20Eldar/Odd%20numbers%20that%20are%20not%20safe%20primes%20such%20that%20p-1%20|%20k-1%20or%20k-1%20|%20p-1%20for%20every%20prime%20p%20|%202^(k-1)-1/prog.sf)
        * [Poulet numbers with a record number of divisors that are also Poulet numbers](./oeis-research/Amiram%20Eldar/Poulet%20numbers%20with%20a%20record%20number%20of%20divisors%20that%20are%20also%20Poulet%20numbers)
            * [prog.sf](./oeis-research/Amiram%20Eldar/Poulet%20numbers%20with%20a%20record%20number%20of%20divisors%20that%20are%20also%20Poulet%20numbers/prog.sf)
        * [Poulet numbers with records of abundancy](./oeis-research/Amiram%20Eldar/Poulet%20numbers%20with%20records%20of%20abundancy)
            * [append factors.pl](./oeis-research/Amiram%20Eldar/Poulet%20numbers%20with%20records%20of%20abundancy/append_factors.pl)
            * [filter.sf](./oeis-research/Amiram%20Eldar/Poulet%20numbers%20with%20records%20of%20abundancy/filter.sf)
            * [from lcm.pl](./oeis-research/Amiram%20Eldar/Poulet%20numbers%20with%20records%20of%20abundancy/from_lcm.pl)
            * [from product.pl](./oeis-research/Amiram%20Eldar/Poulet%20numbers%20with%20records%20of%20abundancy/from_product.pl)
            * [generate.pl](./oeis-research/Amiram%20Eldar/Poulet%20numbers%20with%20records%20of%20abundancy/generate.pl)
            * [lcm.sf](./oeis-research/Amiram%20Eldar/Poulet%20numbers%20with%20records%20of%20abundancy/lcm.sf)
            * [recursive.pl](./oeis-research/Amiram%20Eldar/Poulet%20numbers%20with%20records%20of%20abundancy/recursive.pl)
            * [recursive generate with smooth primes.pl](./oeis-research/Amiram%20Eldar/Poulet%20numbers%20with%20records%20of%20abundancy/recursive_generate_with_smooth_primes.pl)
            * [recursive generation.pl](./oeis-research/Amiram%20Eldar/Poulet%20numbers%20with%20records%20of%20abundancy/recursive_generation.pl)
            * [swap factors.pl](./oeis-research/Amiram%20Eldar/Poulet%20numbers%20with%20records%20of%20abundancy/swap_factors.pl)
        * [Quadratic Mersenne primes for alpha = 2 + sqrt(2)](./oeis-research/Amiram%20Eldar/Quadratic%20Mersenne%20primes%20for%20alpha%20=%202%20+%20sqrt(2))
            * [prog.sf](./oeis-research/Amiram%20Eldar/Quadratic%20Mersenne%20primes%20for%20alpha%20=%202%20+%20sqrt(2)/prog.sf)
        * [Semi-unitary perfect numbers](./oeis-research/Amiram%20Eldar/Semi-unitary%20perfect%20numbers)
            * [prog.pl](./oeis-research/Amiram%20Eldar/Semi-unitary%20perfect%20numbers/prog.pl)
        * [The number of terms of A354558 that are <= 10^n](./oeis-research/Amiram%20Eldar/The%20number%20of%20terms%20of%20A354558%20that%20are%20<=%2010^n)
            * [generate.pl](./oeis-research/Amiram%20Eldar/The%20number%20of%20terms%20of%20A354558%20that%20are%20<=%2010^n/generate.pl)
            * [generate optimized.pl](./oeis-research/Amiram%20Eldar/The%20number%20of%20terms%20of%20A354558%20that%20are%20<=%2010^n/generate_optimized.pl)
            * [prog.pl](./oeis-research/Amiram%20Eldar/The%20number%20of%20terms%20of%20A354558%20that%20are%20<=%2010^n/prog.pl)
            * [prog.sf](./oeis-research/Amiram%20Eldar/The%20number%20of%20terms%20of%20A354558%20that%20are%20<=%2010^n/prog.sf)
            * [verify.sf](./oeis-research/Amiram%20Eldar/The%20number%20of%20terms%20of%20A354558%20that%20are%20<=%2010^n/verify.sf)
        * [Unitary harmonic numbers (A006086) that are not unitary arithmetic numbers (A103826)](./oeis-research/Amiram%20Eldar/Unitary%20harmonic%20numbers%20(A006086)%20that%20are%20not%20unitary%20arithmetic%20numbers%20(A103826))
            * [smooth combinations search.pl](./oeis-research/Amiram%20Eldar/Unitary%20harmonic%20numbers%20(A006086)%20that%20are%20not%20unitary%20arithmetic%20numbers%20(A103826)/smooth_combinations_search.pl)
            * [smooth search.pl](./oeis-research/Amiram%20Eldar/Unitary%20harmonic%20numbers%20(A006086)%20that%20are%20not%20unitary%20arithmetic%20numbers%20(A103826)/smooth_search.pl)
    * [Antti Karttunen](./oeis-research/Antti%20Karttunen)
        * [Numbers k such that derivative(sigma(k)) = k](./oeis-research/Antti%20Karttunen/Numbers%20k%20such%20that%20derivative(sigma(k))%20=%20k)
            * [search.sf](./oeis-research/Antti%20Karttunen/Numbers%20k%20such%20that%20derivative(sigma(k))%20=%20k/search.sf)
            * [search 2.sf](./oeis-research/Antti%20Karttunen/Numbers%20k%20such%20that%20derivative(sigma(k))%20=%20k/search_2.sf)
            * [smooth generate.pl](./oeis-research/Antti%20Karttunen/Numbers%20k%20such%20that%20derivative(sigma(k))%20=%20k/smooth_generate.pl)
    * [Arkadiusz Wesolowski](./oeis-research/Arkadiusz%20Wesolowski)
        * [Numbers k such that phi(binomial(k,2)) is a power of 2](./oeis-research/Arkadiusz%20Wesolowski/Numbers%20k%20such%20that%20phi(binomial(k,2))%20is%20a%20power%20of%202)
            * [prog.sf](./oeis-research/Arkadiusz%20Wesolowski/Numbers%20k%20such%20that%20phi(binomial(k,2))%20is%20a%20power%20of%202/prog.sf)
    * [Arsen Vardanyan](./oeis-research/Arsen%20Vardanyan)
        * [Numbers k such that 29^k - 2 is prime](./oeis-research/Arsen%20Vardanyan/Numbers%20k%20such%20that%2029^k%20-%202%20is%20prime)
            * [prog.sf](./oeis-research/Arsen%20Vardanyan/Numbers%20k%20such%20that%2029^k%20-%202%20is%20prime/prog.sf)
    * [Artsiom Palkounikau](./oeis-research/Artsiom%20Palkounikau)
        * [Smallest k such that 2^(3*2^n) - k is a safe prime](./oeis-research/Artsiom%20Palkounikau/Smallest%20k%20such%20that%202^(3*2^n)%20-%20k%20is%20a%20safe%20prime)
            * [search.pl](./oeis-research/Artsiom%20Palkounikau/Smallest%20k%20such%20that%202^(3*2^n)%20-%20k%20is%20a%20safe%20prime/search.pl)
    * [Artur Jasinski](./oeis-research/Artur%20Jasinski)
        * [A(n) = largest prime divisor of A138957(n)](./oeis-research/Artur%20Jasinski/a(n)%20=%20largest%20prime%20divisor%20of%20A138957(n))
            * [prog.sf](./oeis-research/Artur%20Jasinski/a(n)%20=%20largest%20prime%20divisor%20of%20A138957(n)/prog.sf)
        * [A(n) = smallest number k such that number of prime factors of 2^k-1 is exactly n (counted with multiplicity)](./oeis-research/Artur%20Jasinski/a(n)%20=%20smallest%20number%20k%20such%20that%20number%20of%20prime%20factors%20of%202^k-1%20is%20exactly%20n%20(counted%20with%20multiplicity))
            * [prog.sf](./oeis-research/Artur%20Jasinski/a(n)%20=%20smallest%20number%20k%20such%20that%20number%20of%20prime%20factors%20of%202^k-1%20is%20exactly%20n%20(counted%20with%20multiplicity)/prog.sf)
        * [A(n) = the largest prime divisor of A138793(n)](./oeis-research/Artur%20Jasinski/a(n)%20=%20the%20largest%20prime%20divisor%20of%20A138793(n))
            * [prog.sf](./oeis-research/Artur%20Jasinski/a(n)%20=%20the%20largest%20prime%20divisor%20of%20A138793(n)/prog.sf)
        * [A(n) = the smallest prime divisor of A138793(n)](./oeis-research/Artur%20Jasinski/a(n)%20=%20the%20smallest%20prime%20divisor%20of%20A138793(n))
            * [prog.sf](./oeis-research/Artur%20Jasinski/a(n)%20=%20the%20smallest%20prime%20divisor%20of%20A138793(n)/prog.sf)
    * [Benoit Cloitre](./oeis-research/Benoit%20Cloitre)
        * [Count of k-omega primes <= n](./oeis-research/Benoit%20Cloitre/Count%20of%20k-omega%20primes%20<=%20n)
            * [prog.gp](./oeis-research/Benoit%20Cloitre/Count%20of%20k-omega%20primes%20<=%20n/prog.gp)
        * [Where 11^n occurs in n-almost-primes, starting at a(0)=1](./oeis-research/Benoit%20Cloitre/Where%2011^n%20occurs%20in%20n-almost-primes,%20starting%20at%20a(0)=1)
            * [prog.sf](./oeis-research/Benoit%20Cloitre/Where%2011^n%20occurs%20in%20n-almost-primes,%20starting%20at%20a(0)=1/prog.sf)
    * [Bernard Schott](./oeis-research/Bernard%20Schott)
        * [5^n ends in n](./oeis-research/Bernard%20Schott/5^n%20ends%20in%20n)
            * [prog.pl](./oeis-research/Bernard%20Schott/5^n%20ends%20in%20n/prog.pl)
        * [A(n) is the largest prime < 10^n obtained with the longest sum of consecutive primes](./oeis-research/Bernard%20Schott/a(n)%20is%20the%20largest%20prime%20<%2010^n%20obtained%20with%20the%20longest%20sum%20of%20consecutive%20primes)
            * [prog fast.pl](./oeis-research/Bernard%20Schott/a(n)%20is%20the%20largest%20prime%20<%2010^n%20obtained%20with%20the%20longest%20sum%20of%20consecutive%20primes/prog_fast.pl)
            * [prog slow.pl](./oeis-research/Bernard%20Schott/a(n)%20is%20the%20largest%20prime%20<%2010^n%20obtained%20with%20the%20longest%20sum%20of%20consecutive%20primes/prog_slow.pl)
        * [A(n) is the smallest integer that has exactly n Lucas divisors](./oeis-research/Bernard%20Schott/a(n)%20is%20the%20smallest%20integer%20that%20has%20exactly%20n%20Lucas%20divisors)
            * [prog.pl](./oeis-research/Bernard%20Schott/a(n)%20is%20the%20smallest%20integer%20that%20has%20exactly%20n%20Lucas%20divisors/prog.pl)
            * [prog.sf](./oeis-research/Bernard%20Schott/a(n)%20is%20the%20smallest%20integer%20that%20has%20exactly%20n%20Lucas%20divisors/prog.sf)
            * [upper-bounds.sf](./oeis-research/Bernard%20Schott/a(n)%20is%20the%20smallest%20integer%20that%20has%20exactly%20n%20Lucas%20divisors/upper-bounds.sf)
        * [Brazilian primes constant](./oeis-research/Bernard%20Schott/Brazilian%20primes%20constant)
            * [eff.pl](./oeis-research/Bernard%20Schott/Brazilian%20primes%20constant/eff.pl)
            * [prog.pl](./oeis-research/Bernard%20Schott/Brazilian%20primes%20constant/prog.pl)
        * [Largest prime whose decimal expansion consists of the concatenation of the largest n-digit primes](./oeis-research/Bernard%20Schott/Largest%20prime%20whose%20decimal%20expansion%20consists%20of%20the%20concatenation%20of%20the%20largest%20n-digit%20primes)
            * [prog.sf](./oeis-research/Bernard%20Schott/Largest%20prime%20whose%20decimal%20expansion%20consists%20of%20the%20concatenation%20of%20the%20largest%20n-digit%20primes/prog.sf)
        * [Smallest exclusionary square (A029783) with exactly n distinct prime factors.](./oeis-research/Bernard%20Schott/Smallest%20exclusionary%20square%20(A029783)%20with%20exactly%20n%20distinct%20prime%20factors.)
            * [prog.sf](./oeis-research/Bernard%20Schott/Smallest%20exclusionary%20square%20(A029783)%20with%20exactly%20n%20distinct%20prime%20factors./prog.sf)
            * [upper-bounds.sf](./oeis-research/Bernard%20Schott/Smallest%20exclusionary%20square%20(A029783)%20with%20exactly%20n%20distinct%20prime%20factors./upper-bounds.sf)
            * [upper-bounds 2.sf](./oeis-research/Bernard%20Schott/Smallest%20exclusionary%20square%20(A029783)%20with%20exactly%20n%20distinct%20prime%20factors./upper-bounds_2.sf)
        * [Smallest Niven (or Harshad) number (A005349) with exactly n distinct prime factors](./oeis-research/Bernard%20Schott/Smallest%20Niven%20(or%20Harshad)%20number%20(A005349)%20with%20exactly%20n%20distinct%20prime%20factors)
            * [prog.sf](./oeis-research/Bernard%20Schott/Smallest%20Niven%20(or%20Harshad)%20number%20(A005349)%20with%20exactly%20n%20distinct%20prime%20factors/prog.sf)
        * [Smallest number m such that tau(k) * k = m has n solutions](./oeis-research/Bernard%20Schott/Smallest%20number%20m%20such%20that%20tau(k)%20*%20k%20=%20m%20has%20n%20solutions)
            * [smooth generate.pl](./oeis-research/Bernard%20Schott/Smallest%20number%20m%20such%20that%20tau(k)%20*%20k%20=%20m%20has%20n%20solutions/smooth_generate.pl)
        * [Smallest Zuckerman number (A007602) with exactly n distinct prime factors](./oeis-research/Bernard%20Schott/Smallest%20Zuckerman%20number%20(A007602)%20with%20exactly%20n%20distinct%20prime%20factors)
            * [prog.sf](./oeis-research/Bernard%20Schott/Smallest%20Zuckerman%20number%20(A007602)%20with%20exactly%20n%20distinct%20prime%20factors/prog.sf)
    * [Bodo Zinser](./oeis-research/Bodo%20Zinser)
        * [Numbers which when chopped into one, two or more parts, added and squared result in the same number](./oeis-research/Bodo%20Zinser/Numbers%20which%20when%20chopped%20into%20one,%20two%20or%20more%20parts,%20added%20and%20squared%20result%20in%20the%20same%20number)
            * [representations.sf](./oeis-research/Bodo%20Zinser/Numbers%20which%20when%20chopped%20into%20one,%20two%20or%20more%20parts,%20added%20and%20squared%20result%20in%20the%20same%20number/representations.sf)
            * [search.jl](./oeis-research/Bodo%20Zinser/Numbers%20which%20when%20chopped%20into%20one,%20two%20or%20more%20parts,%20added%20and%20squared%20result%20in%20the%20same%20number/search.jl)
            * [search.pl](./oeis-research/Bodo%20Zinser/Numbers%20which%20when%20chopped%20into%20one,%20two%20or%20more%20parts,%20added%20and%20squared%20result%20in%20the%20same%20number/search.pl)
    * [Brad Clardy](./oeis-research/Brad%20Clardy)
        * [Number of Fermat pseudoprimes between 2^n and 2^(n+1) that are not Carmichael numbers](./oeis-research/Brad%20Clardy/Number%20of%20Fermat%20pseudoprimes%20between%202^n%20and%202^(n+1)%20that%20are%20not%20Carmichael%20numbers)
            * [prog.sf](./oeis-research/Brad%20Clardy/Number%20of%20Fermat%20pseudoprimes%20between%202^n%20and%202^(n+1)%20that%20are%20not%20Carmichael%20numbers/prog.sf)
    * [Chai Wah Wu](./oeis-research/Chai%20Wah%20Wu)
        * [Numbers k such that prime(k)^prime(k+1) == prime(k+2) (mod prime(k+3))](./oeis-research/Chai%20Wah%20Wu/Numbers%20k%20such%20that%20prime(k)^prime(k+1)%20==%20prime(k+2)%20(mod%20prime(k+3)))
            * [prog.pl](./oeis-research/Chai%20Wah%20Wu/Numbers%20k%20such%20that%20prime(k)^prime(k+1)%20==%20prime(k+2)%20(mod%20prime(k+3))/prog.pl)
        * [Smallest palindrome in base 10 whose factorization contains n distinct base 10 palindromic prime factors](./oeis-research/Chai%20Wah%20Wu/Smallest%20palindrome%20in%20base%2010%20whose%20factorization%20contains%20n%20distinct%20base%2010%20palindromic%20prime%20factors)
            * [prog.sf](./oeis-research/Chai%20Wah%20Wu/Smallest%20palindrome%20in%20base%2010%20whose%20factorization%20contains%20n%20distinct%20base%2010%20palindromic%20prime%20factors/prog.sf)
    * [Charles Marsden](./oeis-research/Charles%20Marsden)
        * [Smallest index k such that the k-th prime number in base-2 contains the n-th Fibonacci number in base-2 as a contiguous substring](./oeis-research/Charles%20Marsden/Smallest%20index%20k%20such%20that%20the%20k-th%20prime%20number%20in%20base-2%20contains%20the%20n-th%20Fibonacci%20number%20in%20base-2%20as%20a%20contiguous%20substring)
            * [generate.sf](./oeis-research/Charles%20Marsden/Smallest%20index%20k%20such%20that%20the%20k-th%20prime%20number%20in%20base-2%20contains%20the%20n-th%20Fibonacci%20number%20in%20base-2%20as%20a%20contiguous%20substring/generate.sf)
    * [Charles R Greathouse IV](./oeis-research/Charles%20R%20Greathouse%20IV)
        * [Records for the number of divisors d of n such that d+1 is prime](./oeis-research/Charles%20R%20Greathouse%20IV/Records%20for%20the%20number%20of%20divisors%20d%20of%20n%20such%20that%20d+1%20is%20prime)
            * [prog.pl](./oeis-research/Charles%20R%20Greathouse%20IV/Records%20for%20the%20number%20of%20divisors%20d%20of%20n%20such%20that%20d+1%20is%20prime/prog.pl)
        * [Smallest k such that 2^(2^n) - 2^k - 1 is prime](./oeis-research/Charles%20R%20Greathouse%20IV/Smallest%20k%20such%20that%202^(2^n)%20-%202^k%20-%201%20is%20prime)
            * [search.sf](./oeis-research/Charles%20R%20Greathouse%20IV/Smallest%20k%20such%20that%202^(2^n)%20-%202^k%20-%201%20is%20prime/search.sf)
    * [Charles T. Le](./oeis-research/Charles%20T.%20Le)
        * [Number of prime factors of 1+(n!)^2 (with multiplicity)](./oeis-research/Charles%20T.%20Le/Number%20of%20prime%20factors%20of%201+(n!)^2%20(with%20multiplicity))
            * [prog.sf](./oeis-research/Charles%20T.%20Le/Number%20of%20prime%20factors%20of%201+(n!)^2%20(with%20multiplicity)/prog.sf)
    * [Charlie Neder](./oeis-research/Charlie%20Neder)
        * [Modulo p is strictly increasing over the first n primes](./oeis-research/Charlie%20Neder/Modulo%20p%20is%20strictly%20increasing%20over%20the%20first%20n%20primes)
            * [u.pl](./oeis-research/Charlie%20Neder/Modulo%20p%20is%20strictly%20increasing%20over%20the%20first%20n%20primes/u.pl)
            * [u neg k.pl](./oeis-research/Charlie%20Neder/Modulo%20p%20is%20strictly%20increasing%20over%20the%20first%20n%20primes/u_neg_k.pl)
            * [x.cpp](./oeis-research/Charlie%20Neder/Modulo%20p%20is%20strictly%20increasing%20over%20the%20first%20n%20primes/x.cpp)
            * [x neg k.cpp](./oeis-research/Charlie%20Neder/Modulo%20p%20is%20strictly%20increasing%20over%20the%20first%20n%20primes/x_neg_k.cpp)
    * [Cino Hilliard](./oeis-research/Cino%20Hilliard)
        * [Numbers n such that n^n + 10 is prime](./oeis-research/Cino%20Hilliard/Numbers%20n%20such%20that%20n^n%20+%2010%20is%20prime)
            * [prog.sf](./oeis-research/Cino%20Hilliard/Numbers%20n%20such%20that%20n^n%20+%2010%20is%20prime/prog.sf)
    * [Clark Kimberling](./oeis-research/Clark%20Kimberling)
        * [Least k such that exp(log(1) - log(2)*n) > (exp((lngamma(k+1) + k) - (log(sqrt(2*Pi)) + log(k)*(k + 0.5))) - 1)](./oeis-research/Clark%20Kimberling/Least%20k%20such%20that%20exp(log(1)%20-%20log(2)*n)%20>%20(exp((lngamma(k+1)%20+%20k)%20-%20(log(sqrt(2*Pi))%20+%20log(k)*(k%20+%200.5)))%20-%201))
            * [prog.sf](./oeis-research/Clark%20Kimberling/Least%20k%20such%20that%20exp(log(1)%20-%20log(2)*n)%20>%20(exp((lngamma(k+1)%20+%20k)%20-%20(log(sqrt(2*Pi))%20+%20log(k)*(k%20+%200.5)))%20-%201)/prog.sf)
    * [Claude H. R. Dequatre](./oeis-research/Claude%20H.%20R.%20Dequatre)
        * [Numbers k such that tau(k) + tau(Fibonacci(k)) is in A001248, where tau(k) is the number of divisors of k](./oeis-research/Claude%20H.%20R.%20Dequatre/Numbers%20k%20such%20that%20tau(k)%20+%20tau(Fibonacci(k))%20is%20in%20A001248,%20where%20tau(k)%20is%20the%20number%20of%20divisors%20of%20k)
            * [prog.sf](./oeis-research/Claude%20H.%20R.%20Dequatre/Numbers%20k%20such%20that%20tau(k)%20+%20tau(Fibonacci(k))%20is%20in%20A001248,%20where%20tau(k)%20is%20the%20number%20of%20divisors%20of%20k/prog.sf)
    * [Claudio Meller](./oeis-research/Claudio%20Meller)
        * [English number spellings](./oeis-research/Claudio%20Meller/English%20number%20spellings)
            * [english numbers.pl](./oeis-research/Claudio%20Meller/English%20number%20spellings/english_numbers.pl)
            * [english numbers optimized.pl](./oeis-research/Claudio%20Meller/English%20number%20spellings/english_numbers_optimized.pl)
        * [Spanish numbers spellings](./oeis-research/Claudio%20Meller/Spanish%20numbers%20spellings)
            * [spanish numbers.pl](./oeis-research/Claudio%20Meller/Spanish%20numbers%20spellings/spanish_numbers.pl)
    * [Colin Barker](./oeis-research/Colin%20Barker)
        * [Largest prime factor of 2^(2*n+1)+2^(n+1)+1](./oeis-research/Colin%20Barker/Largest%20prime%20factor%20of%202^(2*n+1)+2^(n+1)+1)
            * [prog.sf](./oeis-research/Colin%20Barker/Largest%20prime%20factor%20of%202^(2*n+1)+2^(n+1)+1/prog.sf)
        * [Largest prime factor of 2^(2*n+1)-2^(n+1)+1](./oeis-research/Colin%20Barker/Largest%20prime%20factor%20of%202^(2*n+1)-2^(n+1)+1)
            * [prog.sf](./oeis-research/Colin%20Barker/Largest%20prime%20factor%20of%202^(2*n+1)-2^(n+1)+1/prog.sf)
        * [Largest prime factor of 4^(2*n+1)+1](./oeis-research/Colin%20Barker/Largest%20prime%20factor%20of%204^(2*n+1)+1)
            * [prog.sf](./oeis-research/Colin%20Barker/Largest%20prime%20factor%20of%204^(2*n+1)+1/prog.sf)
    * [Ctibor O. Zizka](./oeis-research/Ctibor%20O.%20Zizka)
        * [Numbers k such that partial sums of sigma0 are divisible by pillai's function](./oeis-research/Ctibor%20O.%20Zizka/Numbers%20k%20such%20that%20partial%20sums%20of%20sigma0%20are%20divisible%20by%20pillai's%20function)
            * [prog.pl](./oeis-research/Ctibor%20O.%20Zizka/Numbers%20k%20such%20that%20partial%20sums%20of%20sigma0%20are%20divisible%20by%20pillai's%20function/prog.pl)
        * [Sum of floor(n^2 over k^2)](./oeis-research/Ctibor%20O.%20Zizka/Sum%20of%20floor(n^2%20over%20k^2))
            * [prog.sf](./oeis-research/Ctibor%20O.%20Zizka/Sum%20of%20floor(n^2%20over%20k^2)/prog.sf)
    * [César Aguilera](./oeis-research/César%20Aguilera)
        * [Perfect numbers pseudo-relation](./oeis-research/César%20Aguilera/Perfect%20numbers%20pseudo-relation)
            * [prog.sf](./oeis-research/César%20Aguilera/Perfect%20numbers%20pseudo-relation/prog.sf)
    * [Daniel Hoya](./oeis-research/Daniel%20Hoya)
        * [Fibonacci Lucas primes](./oeis-research/Daniel%20Hoya/Fibonacci%20Lucas%20primes)
            * [fib ceil.sf](./oeis-research/Daniel%20Hoya/Fibonacci%20Lucas%20primes/fib_ceil.sf)
            * [fib floor.sf](./oeis-research/Daniel%20Hoya/Fibonacci%20Lucas%20primes/fib_floor.sf)
            * [lucas ceil.sf](./oeis-research/Daniel%20Hoya/Fibonacci%20Lucas%20primes/lucas_ceil.sf)
            * [lucas floor.sf](./oeis-research/Daniel%20Hoya/Fibonacci%20Lucas%20primes/lucas_floor.sf)
            * [prog.sf](./oeis-research/Daniel%20Hoya/Fibonacci%20Lucas%20primes/prog.sf)
    * [Daniel Lignon](./oeis-research/Daniel%20Lignon)
        * [Composite numbers for which the harmonic mean of proper divisors is an integer](./oeis-research/Daniel%20Lignon/Composite%20numbers%20for%20which%20the%20harmonic%20mean%20of%20proper%20divisors%20is%20an%20integer)
            * [conjectured search.pl](./oeis-research/Daniel%20Lignon/Composite%20numbers%20for%20which%20the%20harmonic%20mean%20of%20proper%20divisors%20is%20an%20integer/conjectured_search.pl)
            * [conjectured search.sf](./oeis-research/Daniel%20Lignon/Composite%20numbers%20for%20which%20the%20harmonic%20mean%20of%20proper%20divisors%20is%20an%20integer/conjectured_search.sf)
            * [conjectured search inverse sigma.pl](./oeis-research/Daniel%20Lignon/Composite%20numbers%20for%20which%20the%20harmonic%20mean%20of%20proper%20divisors%20is%20an%20integer/conjectured_search_inverse_sigma.pl)
            * [conjectured search old.pl](./oeis-research/Daniel%20Lignon/Composite%20numbers%20for%20which%20the%20harmonic%20mean%20of%20proper%20divisors%20is%20an%20integer/conjectured_search_old.pl)
            * [conjectured smooth search.pl](./oeis-research/Daniel%20Lignon/Composite%20numbers%20for%20which%20the%20harmonic%20mean%20of%20proper%20divisors%20is%20an%20integer/conjectured_smooth_search.pl)
            * [generate special form.sf](./oeis-research/Daniel%20Lignon/Composite%20numbers%20for%20which%20the%20harmonic%20mean%20of%20proper%20divisors%20is%20an%20integer/generate_special_form.sf)
            * [smooth generate.pl](./oeis-research/Daniel%20Lignon/Composite%20numbers%20for%20which%20the%20harmonic%20mean%20of%20proper%20divisors%20is%20an%20integer/smooth_generate.pl)
    * [Daniel Suteu](./oeis-research/Daniel%20Suteu)
        * [A(1) = a(2) = 1, a(n) is largest prime factor of concatenation of a(n - 2) and a(n - 1)](./oeis-research/Daniel%20Suteu/a(1)%20=%20a(2)%20=%201,%20a(n)%20is%20largest%20prime%20factor%20of%20concatenation%20of%20a(n%20-%202)%20and%20a(n%20-%201))
            * [prog.sf](./oeis-research/Daniel%20Suteu/a(1)%20=%20a(2)%20=%201,%20a(n)%20is%20largest%20prime%20factor%20of%20concatenation%20of%20a(n%20-%202)%20and%20a(n%20-%201)/prog.sf)
        * [Agrawal's conjecture pseudoprimes](./oeis-research/Daniel%20Suteu/Agrawal's%20conjecture%20pseudoprimes)
            * [other bases.pl](./oeis-research/Daniel%20Suteu/Agrawal's%20conjecture%20pseudoprimes/other_bases.pl)
            * [prog.pl](./oeis-research/Daniel%20Suteu/Agrawal's%20conjecture%20pseudoprimes/prog.pl)
        * [Alternating sum of the Mertens function](./oeis-research/Daniel%20Suteu/Alternating%20sum%20of%20the%20Mertens%20function)
            * [indices of zeros.pl](./oeis-research/Daniel%20Suteu/Alternating%20sum%20of%20the%20Mertens%20function/indices_of_zeros.pl)
            * [sequence.sf](./oeis-research/Daniel%20Suteu/Alternating%20sum%20of%20the%20Mertens%20function/sequence.sf)
        * [Carmichael numbers k such that k+1 is divisible by gpf(k)+1](./oeis-research/Daniel%20Suteu/Carmichael%20numbers%20k%20such%20that%20k+1%20is%20divisible%20by%20gpf(k)+1)
            * [prog.pl](./oeis-research/Daniel%20Suteu/Carmichael%20numbers%20k%20such%20that%20k+1%20is%20divisible%20by%20gpf(k)+1/prog.pl)
        * [Carmichael numbers k where records occur for gcd(k-1, lambda(k))](./oeis-research/Daniel%20Suteu/Carmichael%20numbers%20k%20where%20records%20occur%20for%20gcd(k-1,%20lambda(k)))
            * [from file.sf](./oeis-research/Daniel%20Suteu/Carmichael%20numbers%20k%20where%20records%20occur%20for%20gcd(k-1,%20lambda(k))/from_file.sf)
            * [search.sf](./oeis-research/Daniel%20Suteu/Carmichael%20numbers%20k%20where%20records%20occur%20for%20gcd(k-1,%20lambda(k))/search.sf)
        * [Carmichael numbers n where records occur for gpf(n) divided by lpf(n)](./oeis-research/Daniel%20Suteu/Carmichael%20numbers%20n%20where%20records%20occur%20for%20gpf(n)%20divided%20by%20lpf(n))
            * [prog.sf](./oeis-research/Daniel%20Suteu/Carmichael%20numbers%20n%20where%20records%20occur%20for%20gpf(n)%20divided%20by%20lpf(n)/prog.sf)
        * [Carmichael numbers n where records occur for lpf(n) divided by gpf(n)](./oeis-research/Daniel%20Suteu/Carmichael%20numbers%20n%20where%20records%20occur%20for%20lpf(n)%20divided%20by%20gpf(n))
            * [prog.sf](./oeis-research/Daniel%20Suteu/Carmichael%20numbers%20n%20where%20records%20occur%20for%20lpf(n)%20divided%20by%20gpf(n)/prog.sf)
        * [Carmichael-Lucas-Carmichael almost numbers](./oeis-research/Daniel%20Suteu/Carmichael-Lucas-Carmichael%20almost%20numbers)
            * [from carmichael.sf](./oeis-research/Daniel%20Suteu/Carmichael-Lucas-Carmichael%20almost%20numbers/from_carmichael.sf)
            * [search.sf](./oeis-research/Daniel%20Suteu/Carmichael-Lucas-Carmichael%20almost%20numbers/search.sf)
        * [Chernick-Carmichael numbers](./oeis-research/Daniel%20Suteu/Chernick-Carmichael%20numbers)
            * [is chernick carmichael number.pl](./oeis-research/Daniel%20Suteu/Chernick-Carmichael%20numbers/is_chernick_carmichael_number.pl)
            * [Perl program for A317126.pl](./oeis-research/Daniel%20Suteu/Chernick-Carmichael%20numbers/Perl_program_for_A317126.pl)
            * [pp.pl](./oeis-research/Daniel%20Suteu/Chernick-Carmichael%20numbers/pp.pl)
            * [x.pl](./oeis-research/Daniel%20Suteu/Chernick-Carmichael%20numbers/x.pl)
        * [Chernick-Carmichael numbers with 4 or more prime factors](./oeis-research/Daniel%20Suteu/Chernick-Carmichael%20numbers%20with%204%20or%20more%20prime%20factors)
            * [generate extra terms.pl](./oeis-research/Daniel%20Suteu/Chernick-Carmichael%20numbers%20with%204%20or%20more%20prime%20factors/generate_extra_terms.pl)
        * [Chernick-Carmichael numbers with k factors](./oeis-research/Daniel%20Suteu/Chernick-Carmichael%20numbers%20with%20k%20factors)
            * [x.pl](./oeis-research/Daniel%20Suteu/Chernick-Carmichael%20numbers%20with%20k%20factors/x.pl)
        * [Cubic recurence sequence](./oeis-research/Daniel%20Suteu/Cubic%20recurence%20sequence)
            * [x.pl](./oeis-research/Daniel%20Suteu/Cubic%20recurence%20sequence/x.pl)
        * [Difference of 0's and 1's in middle of binary digits](./oeis-research/Daniel%20Suteu/Difference%20of%200's%20and%201's%20in%20middle%20of%20binary%20digits)
            * [prog.sf](./oeis-research/Daniel%20Suteu/Difference%20of%200's%20and%201's%20in%20middle%20of%20binary%20digits/prog.sf)
        * [Digit scrambling sequences](./oeis-research/Daniel%20Suteu/Digit%20scrambling%20sequences)
            * [prog.pl](./oeis-research/Daniel%20Suteu/Digit%20scrambling%20sequences/prog.pl)
        * [Dirichlet convolution of  2^omega(n)*mu(n)^2 with the positive integers](./oeis-research/Daniel%20Suteu/Dirichlet%20convolution%20of%20%202^omega(n)*mu(n)^2%20with%20the%20positive%20integers)
            * [prog.sf](./oeis-research/Daniel%20Suteu/Dirichlet%20convolution%20of%20%202^omega(n)*mu(n)^2%20with%20the%20positive%20integers/prog.sf)
        * [Emirps](./oeis-research/Daniel%20Suteu/Emirps)
            * [emirps to base n.sf](./oeis-research/Daniel%20Suteu/Emirps/emirps_to_base_n.sf)
            * [search.pl](./oeis-research/Daniel%20Suteu/Emirps/search.pl)
        * [Factor sequences](./oeis-research/Daniel%20Suteu/Factor%20sequences)
            * [semiprimes from base and power.sf](./oeis-research/Daniel%20Suteu/Factor%20sequences/semiprimes_from_base_and_power.sf)
        * [Fermat pseudoprimes of the form p*((p-1)*n + 1)](./oeis-research/Daniel%20Suteu/Fermat%20pseudoprimes%20of%20the%20form%20p*((p-1)*n%20+%201))
            * [prog.pl](./oeis-research/Daniel%20Suteu/Fermat%20pseudoprimes%20of%20the%20form%20p*((p-1)*n%20+%201)/prog.pl)
            * [prog.sf](./oeis-research/Daniel%20Suteu/Fermat%20pseudoprimes%20of%20the%20form%20p*((p-1)*n%20+%201)/prog.sf)
        * [First number k such that k + a(i) has n distinct prime factors, for all i < n](./oeis-research/Daniel%20Suteu/First%20number%20k%20such%20that%20k%20+%20a(i)%20has%20n%20distinct%20prime%20factors,%20for%20all%20i%20<%20n)
            * [prog.sf](./oeis-research/Daniel%20Suteu/First%20number%20k%20such%20that%20k%20+%20a(i)%20has%20n%20distinct%20prime%20factors,%20for%20all%20i%20<%20n/prog.sf)
        * [First number k such that k + a(i) is the product of n distinct prime factors, for all i < n](./oeis-research/Daniel%20Suteu/First%20number%20k%20such%20that%20k%20+%20a(i)%20is%20the%20product%20of%20n%20distinct%20prime%20factors,%20for%20all%20i%20<%20n)
            * [prog.pl](./oeis-research/Daniel%20Suteu/First%20number%20k%20such%20that%20k%20+%20a(i)%20is%20the%20product%20of%20n%20distinct%20prime%20factors,%20for%20all%20i%20<%20n/prog.pl)
            * [prog.sf](./oeis-research/Daniel%20Suteu/First%20number%20k%20such%20that%20k%20+%20a(i)%20is%20the%20product%20of%20n%20distinct%20prime%20factors,%20for%20all%20i%20<%20n/prog.sf)
        * [First number k such that the concatenation of a(i) and k has n distinct prime factors, for all i < n](./oeis-research/Daniel%20Suteu/First%20number%20k%20such%20that%20the%20concatenation%20of%20a(i)%20and%20k%20has%20n%20distinct%20prime%20factors,%20for%20all%20i%20<%20n)
            * [prog.sf](./oeis-research/Daniel%20Suteu/First%20number%20k%20such%20that%20the%20concatenation%20of%20a(i)%20and%20k%20has%20n%20distinct%20prime%20factors,%20for%20all%20i%20<%20n/prog.sf)
        * [First number k such that the concatenation of a(i) and k has n prime factors, counted with multiplicity, for all i < n](./oeis-research/Daniel%20Suteu/First%20number%20k%20such%20that%20the%20concatenation%20of%20a(i)%20and%20k%20has%20n%20prime%20factors,%20counted%20with%20multiplicity,%20for%20all%20i%20<%20n)
            * [prog.sf](./oeis-research/Daniel%20Suteu/First%20number%20k%20such%20that%20the%20concatenation%20of%20a(i)%20and%20k%20has%20n%20prime%20factors,%20counted%20with%20multiplicity,%20for%20all%20i%20<%20n/prog.sf)
        * [First number k such that the concatenation of k and a(i) has n distinct prime factors, for all i < n](./oeis-research/Daniel%20Suteu/First%20number%20k%20such%20that%20the%20concatenation%20of%20k%20and%20a(i)%20has%20n%20distinct%20prime%20factors,%20for%20all%20i%20<%20n)
            * [prog.sf](./oeis-research/Daniel%20Suteu/First%20number%20k%20such%20that%20the%20concatenation%20of%20k%20and%20a(i)%20has%20n%20distinct%20prime%20factors,%20for%20all%20i%20<%20n/prog.sf)
        * [First number k such that the concatenation of k and a(i) has n prime factors, counted with multiplicity, for all i < n](./oeis-research/Daniel%20Suteu/First%20number%20k%20such%20that%20the%20concatenation%20of%20k%20and%20a(i)%20has%20n%20prime%20factors,%20counted%20with%20multiplicity,%20for%20all%20i%20<%20n)
            * [prog.sf](./oeis-research/Daniel%20Suteu/First%20number%20k%20such%20that%20the%20concatenation%20of%20k%20and%20a(i)%20has%20n%20prime%20factors,%20counted%20with%20multiplicity,%20for%20all%20i%20<%20n/prog.sf)
        * [Generalized class of primes](./oeis-research/Daniel%20Suteu/Generalized%20class%20of%20primes)
            * [prog.sf](./oeis-research/Daniel%20Suteu/Generalized%20class%20of%20primes/prog.sf)
        * [Incrementally largest numbers n that are the product of primes p such that p+1 divides n](./oeis-research/Daniel%20Suteu/Incrementally%20largest%20numbers%20n%20that%20are%20the%20product%20of%20primes%20p%20such%20that%20p+1%20divides%20n)
            * [pari prog.gp](./oeis-research/Daniel%20Suteu/Incrementally%20largest%20numbers%20n%20that%20are%20the%20product%20of%20primes%20p%20such%20that%20p+1%20divides%20n/pari_prog.gp)
            * [prog.sf](./oeis-research/Daniel%20Suteu/Incrementally%20largest%20numbers%20n%20that%20are%20the%20product%20of%20primes%20p%20such%20that%20p+1%20divides%20n/prog.sf)
        * [Irregular triangle read by rows of integers k such that n AND k != k, for k = 1..n](./oeis-research/Daniel%20Suteu/Irregular%20triangle%20read%20by%20rows%20of%20integers%20k%20such%20that%20n%20AND%20k%20!=%20k,%20for%20k%20=%201..n)
            * [irregular triangle of n AND k != k.sf](./oeis-research/Daniel%20Suteu/Irregular%20triangle%20read%20by%20rows%20of%20integers%20k%20such%20that%20n%20AND%20k%20!=%20k,%20for%20k%20=%201..n/irregular_triangle_of%20n%20AND%20k%20!=%20k.sf)
            * [prog.sf](./oeis-research/Daniel%20Suteu/Irregular%20triangle%20read%20by%20rows%20of%20integers%20k%20such%20that%20n%20AND%20k%20!=%20k,%20for%20k%20=%201..n/prog.sf)
        * [Irregular triangle read by rows of integers k such that n AND k = k, for k = 1..n](./oeis-research/Daniel%20Suteu/Irregular%20triangle%20read%20by%20rows%20of%20integers%20k%20such%20that%20n%20AND%20k%20=%20k,%20for%20k%20=%201..n)
            * [irregular triangle of n AND k = k.sf](./oeis-research/Daniel%20Suteu/Irregular%20triangle%20read%20by%20rows%20of%20integers%20k%20such%20that%20n%20AND%20k%20=%20k,%20for%20k%20=%201..n/irregular_triangle_of%20n%20AND%20k%20=%20k.sf)
            * [prog.sf](./oeis-research/Daniel%20Suteu/Irregular%20triangle%20read%20by%20rows%20of%20integers%20k%20such%20that%20n%20AND%20k%20=%20k,%20for%20k%20=%201..n/prog.sf)
        * [Large smooth semiprime](./oeis-research/Daniel%20Suteu/Large%20smooth%20semiprime)
            * [curiosity.sf](./oeis-research/Daniel%20Suteu/Large%20smooth%20semiprime/curiosity.sf)
        * [Least non-palindromic number k such that k and its digital reversal both are the product of n distinct primes](./oeis-research/Daniel%20Suteu/Least%20non-palindromic%20number%20k%20such%20that%20k%20and%20its%20digital%20reversal%20both%20are%20the%20product%20of%20n%20distinct%20primes)
            * [prog.pl](./oeis-research/Daniel%20Suteu/Least%20non-palindromic%20number%20k%20such%20that%20k%20and%20its%20digital%20reversal%20both%20are%20the%20product%20of%20n%20distinct%20primes/prog.pl)
        * [Least number k such that A002277(k) has exactly n distinct prime factors](./oeis-research/Daniel%20Suteu/Least%20number%20k%20such%20that%20A002277(k)%20has%20exactly%20n%20distinct%20prime%20factors)
            * [prog.sf](./oeis-research/Daniel%20Suteu/Least%20number%20k%20such%20that%20A002277(k)%20has%20exactly%20n%20distinct%20prime%20factors/prog.sf)
        * [Least prime p such that 2*x*(2*x+1) + p produces primes for x=0..n-1 and composite for x=n](./oeis-research/Daniel%20Suteu/Least%20prime%20p%20such%20that%202*x*(2*x+1)%20+%20p%20produces%20primes%20for%20x=0..n-1%20and%20composite%20for%20x=n)
            * [sieve.pl](./oeis-research/Daniel%20Suteu/Least%20prime%20p%20such%20that%202*x*(2*x+1)%20+%20p%20produces%20primes%20for%20x=0..n-1%20and%20composite%20for%20x=n/sieve.pl)
        * [Least prime p such that x*(x+1)*(x+2) + p produces primes for x=0..n-1 and composite for x=n](./oeis-research/Daniel%20Suteu/Least%20prime%20p%20such%20that%20x*(x+1)*(x+2)%20+%20p%20produces%20primes%20for%20x=0..n-1%20and%20composite%20for%20x=n)
            * [sieve.pl](./oeis-research/Daniel%20Suteu/Least%20prime%20p%20such%20that%20x*(x+1)*(x+2)%20+%20p%20produces%20primes%20for%20x=0..n-1%20and%20composite%20for%20x=n/sieve.pl)
        * [Limit for pi ÷ 4](./oeis-research/Daniel%20Suteu/Limit%20for%20pi%20÷%204)
            * [x.pl](./oeis-research/Daniel%20Suteu/Limit%20for%20pi%20÷%204/x.pl)
        * [Liouville sum](./oeis-research/Daniel%20Suteu/Liouville%20sum)
            * [6april.pl](./oeis-research/Daniel%20Suteu/Liouville%20sum/6april.pl)
            * [new.sf](./oeis-research/Daniel%20Suteu/Liouville%20sum/new.sf)
            * [r.sf](./oeis-research/Daniel%20Suteu/Liouville%20sum/r.sf)
            * [u.sf](./oeis-research/Daniel%20Suteu/Liouville%20sum/u.sf)
            * [u2.sf](./oeis-research/Daniel%20Suteu/Liouville%20sum/u2.sf)
            * [x.pl](./oeis-research/Daniel%20Suteu/Liouville%20sum/x.pl)
        * [Moebius transform of dedekind](./oeis-research/Daniel%20Suteu/Moebius%20transform%20of%20dedekind)
            * [prog.sf](./oeis-research/Daniel%20Suteu/Moebius%20transform%20of%20dedekind/prog.sf)
        * [Number k such that tau(k) equals the number of solutions to sigma(x) = k](./oeis-research/Daniel%20Suteu/Number%20k%20such%20that%20tau(k)%20equals%20the%20number%20of%20solutions%20to%20sigma(x)%20=%20k)
            * [prog.sf](./oeis-research/Daniel%20Suteu/Number%20k%20such%20that%20tau(k)%20equals%20the%20number%20of%20solutions%20to%20sigma(x)%20=%20k/prog.sf)
        * [Number of distinct prime factors of sigma(sigma n(n))](./oeis-research/Daniel%20Suteu/Number%20of%20distinct%20prime%20factors%20of%20sigma(sigma_n(n)))
            * [factorizations.sf](./oeis-research/Daniel%20Suteu/Number%20of%20distinct%20prime%20factors%20of%20sigma(sigma_n(n))/factorizations.sf)
            * [prog.sf](./oeis-research/Daniel%20Suteu/Number%20of%20distinct%20prime%20factors%20of%20sigma(sigma_n(n))/prog.sf)
        * [Number of primes factors of the n-th n-powerful number](./oeis-research/Daniel%20Suteu/Number%20of%20primes%20factors%20of%20the%20n-th%20n-powerful%20number)
            * [nth n-powerful.sf](./oeis-research/Daniel%20Suteu/Number%20of%20primes%20factors%20of%20the%20n-th%20n-powerful%20number/nth_n-powerful.sf)
            * [prog.pl](./oeis-research/Daniel%20Suteu/Number%20of%20primes%20factors%20of%20the%20n-th%20n-powerful%20number/prog.pl)
        * [Numbers k such that (prime(k) - composite(k)) == 0 (mod k)](./oeis-research/Daniel%20Suteu/Numbers%20k%20such%20that%20(prime(k)%20-%20composite(k))%20==%200%20(mod%20k))
            * [prog.pl](./oeis-research/Daniel%20Suteu/Numbers%20k%20such%20that%20(prime(k)%20-%20composite(k))%20==%200%20(mod%20k)/prog.pl)
        * [Numbers k such that phi(k) = factorial of sum of digits of k](./oeis-research/Daniel%20Suteu/Numbers%20k%20such%20that%20phi(k)%20=%20factorial%20of%20sum%20of%20digits%20of%20k)
            * [prog.pl](./oeis-research/Daniel%20Suteu/Numbers%20k%20such%20that%20phi(k)%20=%20factorial%20of%20sum%20of%20digits%20of%20k/prog.pl)
        * [Numbers n such that omega(sigma(n,n)) = bigomega(sigma(n,n))](./oeis-research/Daniel%20Suteu/Numbers%20n%20such%20that%20omega(sigma(n,n))%20=%20bigomega(sigma(n,n)))
            * [prog.sf](./oeis-research/Daniel%20Suteu/Numbers%20n%20such%20that%20omega(sigma(n,n))%20=%20bigomega(sigma(n,n))/prog.sf)
        * [Numbers n such that sigma(n)+1 divides n*(tau(n)+1)](./oeis-research/Daniel%20Suteu/Numbers%20n%20such%20that%20sigma(n)+1%20divides%20n*(tau(n)+1))
            * [prog.pl](./oeis-research/Daniel%20Suteu/Numbers%20n%20such%20that%20sigma(n)+1%20divides%20n*(tau(n)+1)/prog.pl)
        * [Odd squarefree composite integers n such that prev prime(p)-1 | n-1 and next prime(p)-1 | n-1 for every p|n](./oeis-research/Daniel%20Suteu/Odd%20squarefree%20composite%20integers%20n%20such%20that%20prev_prime(p)-1%20|%20n-1%20and%20next_prime(p)-1%20|%20n-1%20for%20every%20p|n)
            * [prog.pl](./oeis-research/Daniel%20Suteu/Odd%20squarefree%20composite%20integers%20n%20such%20that%20prev_prime(p)-1%20|%20n-1%20and%20next_prime(p)-1%20|%20n-1%20for%20every%20p|n/prog.pl)
        * [OEIS Conjecture](./oeis-research/Daniel%20Suteu/OEIS%20Conjecture)
            * [test.sf](./oeis-research/Daniel%20Suteu/OEIS%20Conjecture/test.sf)
        * [Other](./oeis-research/Daniel%20Suteu/Other)
            * [Aliquot sequence starting at 276](./oeis-research/Daniel%20Suteu/Other/Aliquot%20sequence%20starting%20at%20276)
                * [prop sigma.sf](./oeis-research/Daniel%20Suteu/Other/Aliquot%20sequence%20starting%20at%20276/prop_sigma.sf)
            * [Semiprimes](./oeis-research/Daniel%20Suteu/Other/Semiprimes)
                * [2^n + 5^n is semiprime.sf](./oeis-research/Daniel%20Suteu/Other/Semiprimes/2^n%20+%205^n%20is%20semiprime.sf)
                * [new search.sf](./oeis-research/Daniel%20Suteu/Other/Semiprimes/new_search.sf)
                * [prog.pl](./oeis-research/Daniel%20Suteu/Other/Semiprimes/prog.pl)
                * [prog.sf](./oeis-research/Daniel%20Suteu/Other/Semiprimes/prog.sf)
                * [prog2.pl](./oeis-research/Daniel%20Suteu/Other/Semiprimes/prog2.pl)
            * [Squarefree 2^d-1 and 2^n-1 not squarefree](./oeis-research/Daniel%20Suteu/Other/Squarefree%202^d-1%20and%202^n-1%20not%20squarefree)
                * [2^k - 1 -- prog.sf](./oeis-research/Daniel%20Suteu/Other/Squarefree%202^d-1%20and%202^n-1%20not%20squarefree/2^k%20-%201%20--%20prog.sf)
                * [3^k - 2^k -- prog.sf](./oeis-research/Daniel%20Suteu/Other/Squarefree%202^d-1%20and%202^n-1%20not%20squarefree/3^k%20-%202^k%20--%20prog.sf)
                * [4^k - 3^k -- prog.sf](./oeis-research/Daniel%20Suteu/Other/Squarefree%202^d-1%20and%202^n-1%20not%20squarefree/4^k%20-%203^k%20--%20prog.sf)
                * [5^k - 4^k -- prog.sf](./oeis-research/Daniel%20Suteu/Other/Squarefree%202^d-1%20and%202^n-1%20not%20squarefree/5^k%20-%204^k%20--%20prog.sf)
                * [7^k - 6^k -- prog.sf](./oeis-research/Daniel%20Suteu/Other/Squarefree%202^d-1%20and%202^n-1%20not%20squarefree/7^k%20-%206^k%20--%20prog.sf)
                * [extra.sf](./oeis-research/Daniel%20Suteu/Other/Squarefree%202^d-1%20and%202^n-1%20not%20squarefree/extra.sf)
            * [Useless results](./oeis-research/Daniel%20Suteu/Other/Useless%20results)
                * [new formula for A062354.sf](./oeis-research/Daniel%20Suteu/Other/Useless%20results/new_formula_for_A062354.sf)
        * [Other programs](./oeis-research/Daniel%20Suteu/Other%20programs)
            * [binary factorization.sf](./oeis-research/Daniel%20Suteu/Other%20programs/binary_factorization.sf)
            * [factor divisor remove.sf](./oeis-research/Daniel%20Suteu/Other%20programs/factor_divisor_remove.sf)
            * [fib like sequence.sf](./oeis-research/Daniel%20Suteu/Other%20programs/fib_like_sequence.sf)
            * [gcd prime count.sf](./oeis-research/Daniel%20Suteu/Other%20programs/gcd_prime_count.sf)
            * [gcd primes count euler phi like.sf](./oeis-research/Daniel%20Suteu/Other%20programs/gcd_primes_count_euler_phi_like.sf)
            * [gold mine.sf](./oeis-research/Daniel%20Suteu/Other%20programs/gold_mine.sf)
            * [gold mine 2.sf](./oeis-research/Daniel%20Suteu/Other%20programs/gold_mine_2.sf)
            * [gold mine simple.sf](./oeis-research/Daniel%20Suteu/Other%20programs/gold_mine_simple.sf)
            * [hamming numbers.pl](./oeis-research/Daniel%20Suteu/Other%20programs/hamming_numbers.pl)
            * [partial sums of omega fast.pl](./oeis-research/Daniel%20Suteu/Other%20programs/partial_sums_of_omega_fast.pl)
            * [prime count is pi.sf](./oeis-research/Daniel%20Suteu/Other%20programs/prime_count_is_pi.sf)
            * [sum factor divisor.sf](./oeis-research/Daniel%20Suteu/Other%20programs/sum_factor_divisor.sf)
        * [Palindromic pseudoprimes in base n](./oeis-research/Daniel%20Suteu/Palindromic%20pseudoprimes%20in%20base%20n)
            * [palindromic generation.pl](./oeis-research/Daniel%20Suteu/Palindromic%20pseudoprimes%20in%20base%20n/palindromic_generation.pl)
        * [Partial sums of 2^(bigomega(n) - omega(n))](./oeis-research/Daniel%20Suteu/Partial%20sums%20of%202^(bigomega(n)%20-%20omega(n)))
            * [prog.sf](./oeis-research/Daniel%20Suteu/Partial%20sums%20of%202^(bigomega(n)%20-%20omega(n))/prog.sf)
        * [Partial sums of dirichlet convolution of the prime characterstic function with itself](./oeis-research/Daniel%20Suteu/Partial%20sums%20of%20dirichlet%20convolution%20of%20the%20prime%20characterstic%20function%20with%20itself)
            * [prog.sf](./oeis-research/Daniel%20Suteu/Partial%20sums%20of%20dirichlet%20convolution%20of%20the%20prime%20characterstic%20function%20with%20itself/prog.sf)
        * [Partial sums of inverse moebius transform of 2^bigomega(n)](./oeis-research/Daniel%20Suteu/Partial%20sums%20of%20inverse%20moebius%20transform%20of%202^bigomega(n))
            * [prog.sf](./oeis-research/Daniel%20Suteu/Partial%20sums%20of%20inverse%20moebius%20transform%20of%202^bigomega(n)/prog.sf)
        * [Partial sums of moebius inversion of (-1)^omega](./oeis-research/Daniel%20Suteu/Partial%20sums%20of%20moebius%20inversion%20of%20(-1)^omega)
            * [prog.sf](./oeis-research/Daniel%20Suteu/Partial%20sums%20of%20moebius%20inversion%20of%20(-1)^omega/prog.sf)
        * [Partial sums of sums of prime powers](./oeis-research/Daniel%20Suteu/Partial%20sums%20of%20sums%20of%20prime%20powers)
            * [prog.sf](./oeis-research/Daniel%20Suteu/Partial%20sums%20of%20sums%20of%20prime%20powers/prog.sf)
        * [Records of sigma0 for  p^2-1](./oeis-research/Daniel%20Suteu/Records%20of%20sigma0%20for%20%20p^2-1)
            * [x.pl](./oeis-research/Daniel%20Suteu/Records%20of%20sigma0%20for%20%20p^2-1/x.pl)
        * [Reversal of prime p is composite in all bases 2..n](./oeis-research/Daniel%20Suteu/Reversal%20of%20prime%20p%20is%20composite%20in%20all%20bases%202..n)
            * [prog.sf](./oeis-research/Daniel%20Suteu/Reversal%20of%20prime%20p%20is%20composite%20in%20all%20bases%202..n/prog.sf)
        * [Riemann prime counting function](./oeis-research/Daniel%20Suteu/Riemann%20prime%20counting%20function)
            * [prog.pl](./oeis-research/Daniel%20Suteu/Riemann%20prime%20counting%20function/prog.pl)
        * [Romanian numbers](./oeis-research/Daniel%20Suteu/Romanian%20numbers)
            * [faster.pl](./oeis-research/Daniel%20Suteu/Romanian%20numbers/faster.pl)
            * [search.pl](./oeis-research/Daniel%20Suteu/Romanian%20numbers/search.pl)
        * [Sierpiński triangle](./oeis-research/Daniel%20Suteu/Sierpiński%20triangle)
            * [sierpiński triangle.sf](./oeis-research/Daniel%20Suteu/Sierpiński%20triangle/sierpiński_triangle.sf)
        * [Smallest base-n strong Fermat pseudoprime with n distinct prime factors](./oeis-research/Daniel%20Suteu/Smallest%20base-n%20strong%20Fermat%20pseudoprime%20with%20n%20distinct%20prime%20factors)
            * [prog.pl](./oeis-research/Daniel%20Suteu/Smallest%20base-n%20strong%20Fermat%20pseudoprime%20with%20n%20distinct%20prime%20factors/prog.pl)
            * [prog.sf](./oeis-research/Daniel%20Suteu/Smallest%20base-n%20strong%20Fermat%20pseudoprime%20with%20n%20distinct%20prime%20factors/prog.sf)
            * [prog-squarefree.pl](./oeis-research/Daniel%20Suteu/Smallest%20base-n%20strong%20Fermat%20pseudoprime%20with%20n%20distinct%20prime%20factors/prog-squarefree.pl)
        * [Smallest Carmichael number (A002997) with n prime factors that is also a strong pseudoprime to base 2 (A001262)](./oeis-research/Daniel%20Suteu/Smallest%20Carmichael%20number%20(A002997)%20with%20n%20prime%20factors%20that%20is%20also%20a%20strong%20pseudoprime%20to%20base%202%20(A001262))
            * [prog.pl](./oeis-research/Daniel%20Suteu/Smallest%20Carmichael%20number%20(A002997)%20with%20n%20prime%20factors%20that%20is%20also%20a%20strong%20pseudoprime%20to%20base%202%20(A001262)/prog.pl)
            * [prog faster.pl](./oeis-research/Daniel%20Suteu/Smallest%20Carmichael%20number%20(A002997)%20with%20n%20prime%20factors%20that%20is%20also%20a%20strong%20pseudoprime%20to%20base%202%20(A001262)/prog_faster.pl)
        * [Smallest Carmichael number such that gpf(p-1) = prime(n)](./oeis-research/Daniel%20Suteu/Smallest%20Carmichael%20number%20such%20that%20gpf(p-1)%20=%20prime(n))
            * [check.sf](./oeis-research/Daniel%20Suteu/Smallest%20Carmichael%20number%20such%20that%20gpf(p-1)%20=%20prime(n)/check.sf)
            * [from psp.pl](./oeis-research/Daniel%20Suteu/Smallest%20Carmichael%20number%20such%20that%20gpf(p-1)%20=%20prime(n)/from_psp.pl)
            * [prog.sf](./oeis-research/Daniel%20Suteu/Smallest%20Carmichael%20number%20such%20that%20gpf(p-1)%20=%20prime(n)/prog.sf)
            * [sort.pl](./oeis-research/Daniel%20Suteu/Smallest%20Carmichael%20number%20such%20that%20gpf(p-1)%20=%20prime(n)/sort.pl)
            * [upper bounds.sf](./oeis-research/Daniel%20Suteu/Smallest%20Carmichael%20number%20such%20that%20gpf(p-1)%20=%20prime(n)/upper_bounds.sf)
            * [upper bounds 2.sf](./oeis-research/Daniel%20Suteu/Smallest%20Carmichael%20number%20such%20that%20gpf(p-1)%20=%20prime(n)/upper_bounds_2.sf)
        * [Smallest Fermat base-2 pseudoprime such that gpf(p-1) = prime(n)](./oeis-research/Daniel%20Suteu/Smallest%20Fermat%20base-2%20pseudoprime%20such%20that%20gpf(p-1)%20=%20prime(n))
            * [check.sf](./oeis-research/Daniel%20Suteu/Smallest%20Fermat%20base-2%20pseudoprime%20such%20that%20gpf(p-1)%20=%20prime(n)/check.sf)
            * [prog.sf](./oeis-research/Daniel%20Suteu/Smallest%20Fermat%20base-2%20pseudoprime%20such%20that%20gpf(p-1)%20=%20prime(n)/prog.sf)
            * [smooth.pl](./oeis-research/Daniel%20Suteu/Smallest%20Fermat%20base-2%20pseudoprime%20such%20that%20gpf(p-1)%20=%20prime(n)/smooth.pl)
            * [upper bounds.sf](./oeis-research/Daniel%20Suteu/Smallest%20Fermat%20base-2%20pseudoprime%20such%20that%20gpf(p-1)%20=%20prime(n)/upper_bounds.sf)
        * [Smallest number k > 0 such that bigomega(k^n + 1) = n](./oeis-research/Daniel%20Suteu/Smallest%20number%20k%20>%200%20such%20that%20bigomega(k^n%20+%201)%20=%20n)
            * [prog.sf](./oeis-research/Daniel%20Suteu/Smallest%20number%20k%20>%200%20such%20that%20bigomega(k^n%20+%201)%20=%20n/prog.sf)
        * [Smallest number k > 1 such that bigomega(k^n - 1) = n](./oeis-research/Daniel%20Suteu/Smallest%20number%20k%20>%201%20such%20that%20bigomega(k^n%20-%201)%20=%20n)
            * [prog.sf](./oeis-research/Daniel%20Suteu/Smallest%20number%20k%20>%201%20such%20that%20bigomega(k^n%20-%201)%20=%20n/prog.sf)
            * [upper-bounds.sf](./oeis-research/Daniel%20Suteu/Smallest%20number%20k%20>%201%20such%20that%20bigomega(k^n%20-%201)%20=%20n/upper-bounds.sf)
        * [Smallest overpseudoprime to base 2 (A141232) with n distinct prime factors](./oeis-research/Daniel%20Suteu/Smallest%20overpseudoprime%20to%20base%202%20(A141232)%20with%20n%20distinct%20prime%20factors)
            * [prog.pl](./oeis-research/Daniel%20Suteu/Smallest%20overpseudoprime%20to%20base%202%20(A141232)%20with%20n%20distinct%20prime%20factors/prog.pl)
            * [prog.sf](./oeis-research/Daniel%20Suteu/Smallest%20overpseudoprime%20to%20base%202%20(A141232)%20with%20n%20distinct%20prime%20factors/prog.sf)
            * [prog faster.pl](./oeis-research/Daniel%20Suteu/Smallest%20overpseudoprime%20to%20base%202%20(A141232)%20with%20n%20distinct%20prime%20factors/prog_faster.pl)
            * [upper-bounds.sf](./oeis-research/Daniel%20Suteu/Smallest%20overpseudoprime%20to%20base%202%20(A141232)%20with%20n%20distinct%20prime%20factors/upper-bounds.sf)
            * [upper-bounds-faster.sf](./oeis-research/Daniel%20Suteu/Smallest%20overpseudoprime%20to%20base%202%20(A141232)%20with%20n%20distinct%20prime%20factors/upper-bounds-faster.sf)
        * [Smallest palindrome with n prime factors](./oeis-research/Daniel%20Suteu/Smallest%20palindrome%20with%20n%20prime%20factors)
            * [prog.sf](./oeis-research/Daniel%20Suteu/Smallest%20palindrome%20with%20n%20prime%20factors/prog.sf)
        * [Smallest prime p such that omega(p^n + 1) = n](./oeis-research/Daniel%20Suteu/Smallest%20prime%20p%20such%20that%20omega(p^n%20+%201)%20=%20n)
            * [prog.sf](./oeis-research/Daniel%20Suteu/Smallest%20prime%20p%20such%20that%20omega(p^n%20+%201)%20=%20n/prog.sf)
        * [Smallest squarefree palindrome with exactly n distinct palindromic prime factors](./oeis-research/Daniel%20Suteu/Smallest%20squarefree%20palindrome%20with%20exactly%20n%20distinct%20palindromic%20prime%20factors)
            * [prog.sf](./oeis-research/Daniel%20Suteu/Smallest%20squarefree%20palindrome%20with%20exactly%20n%20distinct%20palindromic%20prime%20factors/prog.sf)
            * [squarefree omega palindromes.jl](./oeis-research/Daniel%20Suteu/Smallest%20squarefree%20palindrome%20with%20exactly%20n%20distinct%20palindromic%20prime%20factors/squarefree_omega_palindromes.jl)
        * [Square array A(n, k) read by antidiagonals downwards: smallest base-n strong Fermat pseudoprime with k distinct prime factors for k, n >= 2](./oeis-research/Daniel%20Suteu/Square%20array%20A(n,%20k)%20read%20by%20antidiagonals%20downwards:%20smallest%20base-n%20strong%20Fermat%20pseudoprime%20with%20k%20distinct%20prime%20factors%20for%20k,%20n%20>=%202)
            * [prog.pl](./oeis-research/Daniel%20Suteu/Square%20array%20A(n,%20k)%20read%20by%20antidiagonals%20downwards:%20smallest%20base-n%20strong%20Fermat%20pseudoprime%20with%20k%20distinct%20prime%20factors%20for%20k,%20n%20>=%202/prog.pl)
            * [prog.sf](./oeis-research/Daniel%20Suteu/Square%20array%20A(n,%20k)%20read%20by%20antidiagonals%20downwards:%20smallest%20base-n%20strong%20Fermat%20pseudoprime%20with%20k%20distinct%20prime%20factors%20for%20k,%20n%20>=%202/prog.sf)
            * [verify terms.sf](./oeis-research/Daniel%20Suteu/Square%20array%20A(n,%20k)%20read%20by%20antidiagonals%20downwards:%20smallest%20base-n%20strong%20Fermat%20pseudoprime%20with%20k%20distinct%20prime%20factors%20for%20k,%20n%20>=%202/verify_terms.sf)
        * [Surprising chaotic finite sequence](./oeis-research/Daniel%20Suteu/Surprising%20chaotic%20finite%20sequence)
            * [prog.sf](./oeis-research/Daniel%20Suteu/Surprising%20chaotic%20finite%20sequence/prog.sf)
        * [TODO](./oeis-research/Daniel%20Suteu/TODO)
            * [Add new terms to A076960](./oeis-research/Daniel%20Suteu/TODO/Add%20new%20terms%20to%20A076960)
                * [the number of primes between factorial(n) and factorial(2n).sf](./oeis-research/Daniel%20Suteu/TODO/Add%20new%20terms%20to%20A076960/the%20number%20of%20primes%20between%20factorial(n)%20and%20factorial(2n).sf)
            * [Add terms to A305058](./oeis-research/Daniel%20Suteu/TODO/Add%20terms%20to%20A305058)
                * [prog.pl](./oeis-research/Daniel%20Suteu/TODO/Add%20terms%20to%20A305058/prog.pl)
                * [prog2.pl](./oeis-research/Daniel%20Suteu/TODO/Add%20terms%20to%20A305058/prog2.pl)
                * [prog3.pl](./oeis-research/Daniel%20Suteu/TODO/Add%20terms%20to%20A305058/prog3.pl)
            * [Factorization of  n^n-(n-1)^(n-1)](./oeis-research/Daniel%20Suteu/TODO/Factorization%20of%20%20n^n-(n-1)^(n-1))
                * [prog.pl](./oeis-research/Daniel%20Suteu/TODO/Factorization%20of%20%20n^n-(n-1)^(n-1)/prog.pl)
            * [Factorization of n^n + (n+1)^(n+1)](./oeis-research/Daniel%20Suteu/TODO/Factorization%20of%20n^n%20+%20(n+1)^(n+1))
                * [check.pl](./oeis-research/Daniel%20Suteu/TODO/Factorization%20of%20n^n%20+%20(n+1)^(n+1)/check.pl)
                * [check2.pl](./oeis-research/Daniel%20Suteu/TODO/Factorization%20of%20n^n%20+%20(n+1)^(n+1)/check2.pl)
                * [prog.pl](./oeis-research/Daniel%20Suteu/TODO/Factorization%20of%20n^n%20+%20(n+1)^(n+1)/prog.pl)
            * [Is power plus minus](./oeis-research/Daniel%20Suteu/TODO/Is%20power%20plus%20minus)
                * [p.sf](./oeis-research/Daniel%20Suteu/TODO/Is%20power%20plus%20minus/p.sf)
                * [x.pl](./oeis-research/Daniel%20Suteu/TODO/Is%20power%20plus%20minus/x.pl)
                * [y.pl](./oeis-research/Daniel%20Suteu/TODO/Is%20power%20plus%20minus/y.pl)
            * [Iterative functions - Sidef](./oeis-research/Daniel%20Suteu/TODO/Iterative%20functions%20-%20Sidef)
                * [prog.sf](./oeis-research/Daniel%20Suteu/TODO/Iterative%20functions%20-%20Sidef/prog.sf)
            * [More terms for continued fractions periods](./oeis-research/Daniel%20Suteu/TODO/More%20terms%20for%20continued%20fractions%20periods)
                * [period of continued fraction for square roots.pl](./oeis-research/Daniel%20Suteu/TODO/More%20terms%20for%20continued%20fractions%20periods/period_of_continued_fraction_for_square_roots.pl)
            * [Number of 0's minus number of 1's binary](./oeis-research/Daniel%20Suteu/TODO/Number%20of%200's%20minus%20number%20of%201's%20binary)
                * [prog.sf](./oeis-research/Daniel%20Suteu/TODO/Number%20of%200's%20minus%20number%20of%201's%20binary/prog.sf)
            * [Prime p such that p-1 has a record number of divisors d such that 2^d == 1 mod p](./oeis-research/Daniel%20Suteu/TODO/Prime%20p%20such%20that%20p-1%20has%20a%20record%20number%20of%20divisors%20d%20such%20that%202^d%20==%201%20mod%20p)
                * [prog.sf](./oeis-research/Daniel%20Suteu/TODO/Prime%20p%20such%20that%20p-1%20has%20a%20record%20number%20of%20divisors%20d%20such%20that%202^d%20==%201%20mod%20p/prog.sf)
            * [Primes between composite numbers](./oeis-research/Daniel%20Suteu/TODO/Primes%20between%20composite%20numbers)
                * [prog.pl](./oeis-research/Daniel%20Suteu/TODO/Primes%20between%20composite%20numbers/prog.pl)
    * [Darío Clavijo](./oeis-research/Darío%20Clavijo)
        * [Numbers k such that k! + k^3 + 1 is prime](./oeis-research/Darío%20Clavijo/Numbers%20k%20such%20that%20k!%20+%20k^3%20+%201%20is%20prime)
            * [prog.sf](./oeis-research/Darío%20Clavijo/Numbers%20k%20such%20that%20k!%20+%20k^3%20+%201%20is%20prime/prog.sf)
    * [David James Sycamore](./oeis-research/David%20James%20Sycamore)
        * [Carmichael divisible by sum of factors](./oeis-research/David%20James%20Sycamore/Carmichael%20divisible%20by%20sum%20of%20factors)
            * [prog.pl](./oeis-research/David%20James%20Sycamore/Carmichael%20divisible%20by%20sum%20of%20factors/prog.pl)
        * [Numbers k such that if j is the sum of the first k primes, then the sum of the first j primes is prime](./oeis-research/David%20James%20Sycamore/Numbers%20k%20such%20that%20if%20j%20is%20the%20sum%20of%20the%20first%20k%20primes,%20then%20the%20sum%20of%20the%20first%20j%20primes%20is%20prime)
            * [prog.pl](./oeis-research/David%20James%20Sycamore/Numbers%20k%20such%20that%20if%20j%20is%20the%20sum%20of%20the%20first%20k%20primes,%20then%20the%20sum%20of%20the%20first%20j%20primes%20is%20prime/prog.pl)
        * [Numbers k such that prime(k)^k - primorial(k - 1) is prime](./oeis-research/David%20James%20Sycamore/Numbers%20k%20such%20that%20prime(k)^k%20-%20primorial(k%20-%201)%20is%20prime)
            * [prog.pl](./oeis-research/David%20James%20Sycamore/Numbers%20k%20such%20that%20prime(k)^k%20-%20primorial(k%20-%201)%20is%20prime/prog.pl)
        * [Prime indexed primes](./oeis-research/David%20James%20Sycamore/Prime%20indexed%20primes)
            * [prog.pl](./oeis-research/David%20James%20Sycamore/Prime%20indexed%20primes/prog.pl)
        * [Primes p such that if k is the sum of the first p primes then the sum of the first k primes is prime](./oeis-research/David%20James%20Sycamore/Primes%20p%20such%20that%20if%20k%20is%20the%20sum%20of%20the%20first%20p%20primes%20then%20the%20sum%20of%20the%20first%20k%20primes%20is%20prime)
            * [prog.pl](./oeis-research/David%20James%20Sycamore/Primes%20p%20such%20that%20if%20k%20is%20the%20sum%20of%20the%20first%20p%20primes%20then%20the%20sum%20of%20the%20first%20k%20primes%20is%20prime/prog.pl)
        * [Smallest prime number whose a056240-type is n](./oeis-research/David%20James%20Sycamore/Smallest%20prime%20number%20whose%20a056240-type%20is%20n)
            * [v1.pl](./oeis-research/David%20James%20Sycamore/Smallest%20prime%20number%20whose%20a056240-type%20is%20n/v1.pl)
            * [v2.pl](./oeis-research/David%20James%20Sycamore/Smallest%20prime%20number%20whose%20a056240-type%20is%20n/v2.pl)
    * [Davide Rotondo](./oeis-research/Davide%20Rotondo)
        * [Primorial conjecture](./oeis-research/Davide%20Rotondo/Primorial%20conjecture)
            * [prog.sf](./oeis-research/Davide%20Rotondo/Primorial%20conjecture/prog.sf)
    * [Derek Orr](./oeis-research/Derek%20Orr)
        * [Least number k such that k^n and k^n-1 contain the same number of prime factors (counted with multiplicity) or 0 if no such k exists](./oeis-research/Derek%20Orr/Least%20number%20k%20such%20that%20k^n%20and%20k^n-1%20contain%20the%20same%20number%20of%20prime%20factors%20(counted%20with%20multiplicity)%20or%200%20if%20no%20such%20k%20exists)
            * [is almost prime.sf](./oeis-research/Derek%20Orr/Least%20number%20k%20such%20that%20k^n%20and%20k^n-1%20contain%20the%20same%20number%20of%20prime%20factors%20(counted%20with%20multiplicity)%20or%200%20if%20no%20such%20k%20exists/is_almost_prime.sf)
            * [prog.sf](./oeis-research/Derek%20Orr/Least%20number%20k%20such%20that%20k^n%20and%20k^n-1%20contain%20the%20same%20number%20of%20prime%20factors%20(counted%20with%20multiplicity)%20or%200%20if%20no%20such%20k%20exists/prog.sf)
            * [prog simple.sf](./oeis-research/Derek%20Orr/Least%20number%20k%20such%20that%20k^n%20and%20k^n-1%20contain%20the%20same%20number%20of%20prime%20factors%20(counted%20with%20multiplicity)%20or%200%20if%20no%20such%20k%20exists/prog_simple.sf)
        * [Least prime p such that p^n and p^n+1 have the same number of prime factors (counted with multiplicity) or 0 if no such number exists](./oeis-research/Derek%20Orr/Least%20prime%20p%20such%20that%20p^n%20and%20p^n+1%20have%20the%20same%20number%20of%20prime%20factors%20(counted%20with%20multiplicity)%20or%200%20if%20no%20such%20number%20exists)
            * [is almost prime.sf](./oeis-research/Derek%20Orr/Least%20prime%20p%20such%20that%20p^n%20and%20p^n+1%20have%20the%20same%20number%20of%20prime%20factors%20(counted%20with%20multiplicity)%20or%200%20if%20no%20such%20number%20exists/is_almost_prime.sf)
            * [prog.sf](./oeis-research/Derek%20Orr/Least%20prime%20p%20such%20that%20p^n%20and%20p^n+1%20have%20the%20same%20number%20of%20prime%20factors%20(counted%20with%20multiplicity)%20or%200%20if%20no%20such%20number%20exists/prog.sf)
            * [simple prog.sf](./oeis-research/Derek%20Orr/Least%20prime%20p%20such%20that%20p^n%20and%20p^n+1%20have%20the%20same%20number%20of%20prime%20factors%20(counted%20with%20multiplicity)%20or%200%20if%20no%20such%20number%20exists/simple_prog.sf)
            * [upper-bounds.sf](./oeis-research/Derek%20Orr/Least%20prime%20p%20such%20that%20p^n%20and%20p^n+1%20have%20the%20same%20number%20of%20prime%20factors%20(counted%20with%20multiplicity)%20or%200%20if%20no%20such%20number%20exists/upper-bounds.sf)
        * [Smallest number m such that m and reverse(m) each have n distinct prime factors](./oeis-research/Derek%20Orr/Smallest%20number%20m%20such%20that%20m%20and%20reverse(m)%20each%20have%20n%20distinct%20prime%20factors)
            * [omega generate.jl](./oeis-research/Derek%20Orr/Smallest%20number%20m%20such%20that%20m%20and%20reverse(m)%20each%20have%20n%20distinct%20prime%20factors/omega_generate.jl)
            * [prog.sf](./oeis-research/Derek%20Orr/Smallest%20number%20m%20such%20that%20m%20and%20reverse(m)%20each%20have%20n%20distinct%20prime%20factors/prog.sf)
    * [Donovan Johnson](./oeis-research/Donovan%20Johnson)
        * [Smallest number m such that sigma(m) has exactly n distinct prime factors](./oeis-research/Donovan%20Johnson/Smallest%20number%20m%20such%20that%20sigma(m)%20has%20exactly%20n%20distinct%20prime%20factors)
            * [upper-bounds.sf](./oeis-research/Donovan%20Johnson/Smallest%20number%20m%20such%20that%20sigma(m)%20has%20exactly%20n%20distinct%20prime%20factors/upper-bounds.sf)
    * [Eder Vanzei](./oeis-research/Eder%20Vanzei)
        * [Primes of the form concatenation(n (once), n-1 (twice), n-2 (3 times), ..., 1 (n times))](./oeis-research/Eder%20Vanzei/Primes%20of%20the%20form%20concatenation(n%20(once),%20n-1%20(twice),%20n-2%20(3%20times),%20...,%201%20(n%20times)))
            * [prog.sf](./oeis-research/Eder%20Vanzei/Primes%20of%20the%20form%20concatenation(n%20(once),%20n-1%20(twice),%20n-2%20(3%20times),%20...,%201%20(n%20times))/prog.sf)
    * [Eduard Roure Perdices](./oeis-research/Eduard%20Roure%20Perdices)
        * [Largest nonnegative integer m such that m - pi(m) >= pi(m)^(1+inv(n))](./oeis-research/Eduard%20Roure%20Perdices/Largest%20nonnegative%20integer%20m%20such%20that%20m%20-%20pi(m)%20>=%20pi(m)^(1+inv(n)))
            * [binary search.sf](./oeis-research/Eduard%20Roure%20Perdices/Largest%20nonnegative%20integer%20m%20such%20that%20m%20-%20pi(m)%20>=%20pi(m)^(1+inv(n))/binary_search.sf)
            * [binary search approx.sf](./oeis-research/Eduard%20Roure%20Perdices/Largest%20nonnegative%20integer%20m%20such%20that%20m%20-%20pi(m)%20>=%20pi(m)^(1+inv(n))/binary_search_approx.sf)
            * [check.sf](./oeis-research/Eduard%20Roure%20Perdices/Largest%20nonnegative%20integer%20m%20such%20that%20m%20-%20pi(m)%20>=%20pi(m)^(1+inv(n))/check.sf)
            * [linear search.sf](./oeis-research/Eduard%20Roure%20Perdices/Largest%20nonnegative%20integer%20m%20such%20that%20m%20-%20pi(m)%20>=%20pi(m)^(1+inv(n))/linear_search.sf)
        * [Largest nonnegative integer m such that m >= pi(m)^(1 + inv(n))](./oeis-research/Eduard%20Roure%20Perdices/Largest%20nonnegative%20integer%20m%20such%20that%20m%20>=%20pi(m)^(1%20+%20inv(n)))
            * [binary search.sf](./oeis-research/Eduard%20Roure%20Perdices/Largest%20nonnegative%20integer%20m%20such%20that%20m%20>=%20pi(m)^(1%20+%20inv(n))/binary_search.sf)
            * [binary search approx.sf](./oeis-research/Eduard%20Roure%20Perdices/Largest%20nonnegative%20integer%20m%20such%20that%20m%20>=%20pi(m)^(1%20+%20inv(n))/binary_search_approx.sf)
            * [check.sf](./oeis-research/Eduard%20Roure%20Perdices/Largest%20nonnegative%20integer%20m%20such%20that%20m%20>=%20pi(m)^(1%20+%20inv(n))/check.sf)
            * [linear search.sf](./oeis-research/Eduard%20Roure%20Perdices/Largest%20nonnegative%20integer%20m%20such%20that%20m%20>=%20pi(m)^(1%20+%20inv(n))/linear_search.sf)
    * [Elliott Line](./oeis-research/Elliott%20Line)
        * [Pascal-Fibonacci triangle](./oeis-research/Elliott%20Line/Pascal-Fibonacci%20triangle)
            * [fast.cpp](./oeis-research/Elliott%20Line/Pascal-Fibonacci%20triangle/fast.cpp)
            * [prog.pl](./oeis-research/Elliott%20Line/Pascal-Fibonacci%20triangle/prog.pl)
            * [u.pl](./oeis-research/Elliott%20Line/Pascal-Fibonacci%20triangle/u.pl)
            * [v.pl](./oeis-research/Elliott%20Line/Pascal-Fibonacci%20triangle/v.pl)
            * [x.cpp](./oeis-research/Elliott%20Line/Pascal-Fibonacci%20triangle/x.cpp)
    * [Erich Friedman](./oeis-research/Erich%20Friedman)
        * [A(1) = a(2) = 1, a(n) is largest prime factor of concatenation of a(n - 2) and a(n - 1)](./oeis-research/Erich%20Friedman/a(1)%20=%20a(2)%20=%201,%20a(n)%20is%20largest%20prime%20factor%20of%20concatenation%20of%20a(n%20-%202)%20and%20a(n%20-%201))
            * [prog.sf](./oeis-research/Erich%20Friedman/a(1)%20=%20a(2)%20=%201,%20a(n)%20is%20largest%20prime%20factor%20of%20concatenation%20of%20a(n%20-%202)%20and%20a(n%20-%201)/prog.sf)
        * [Squares that remain squares if you decrease every digit by 1](./oeis-research/Erich%20Friedman/Squares%20that%20remain%20squares%20if%20you%20decrease%20every%20digit%20by%201)
            * [prog.pl](./oeis-research/Erich%20Friedman/Squares%20that%20remain%20squares%20if%20you%20decrease%20every%20digit%20by%201/prog.pl)
            * [prog heuristic.pl](./oeis-research/Erich%20Friedman/Squares%20that%20remain%20squares%20if%20you%20decrease%20every%20digit%20by%201/prog_heuristic.pl)
    * [Falcon Shapiro](./oeis-research/Falcon%20Shapiro)
        * [Smallest number that requires at least n distinct repdigits to sum](./oeis-research/Falcon%20Shapiro/Smallest%20number%20that%20requires%20at%20least%20n%20distinct%20repdigits%20to%20sum)
            * [prog.pl](./oeis-research/Falcon%20Shapiro/Smallest%20number%20that%20requires%20at%20least%20n%20distinct%20repdigits%20to%20sum/prog.pl)
            * [prog.sf](./oeis-research/Falcon%20Shapiro/Smallest%20number%20that%20requires%20at%20least%20n%20distinct%20repdigits%20to%20sum/prog.sf)
        * [Smallest number that requires at least n repdigits (not necessary distinct) to sum](./oeis-research/Falcon%20Shapiro/Smallest%20number%20that%20requires%20at%20least%20n%20repdigits%20(not%20necessary%20distinct)%20to%20sum)
            * [prog.sf](./oeis-research/Falcon%20Shapiro/Smallest%20number%20that%20requires%20at%20least%20n%20repdigits%20(not%20necessary%20distinct)%20to%20sum/prog.sf)
    * [Farideh Firoozbakht](./oeis-research/Farideh%20Firoozbakht)
        * [Concatenation of first n primes joined with 0 is prime](./oeis-research/Farideh%20Firoozbakht/Concatenation%20of%20first%20n%20primes%20joined%20with%200%20is%20prime)
            * [prog.sf](./oeis-research/Farideh%20Firoozbakht/Concatenation%20of%20first%20n%20primes%20joined%20with%200%20is%20prime/prog.sf)
        * [Numbers n such that n+sigma(n) is a repunit number](./oeis-research/Farideh%20Firoozbakht/Numbers%20n%20such%20that%20n+sigma(n)%20is%20a%20repunit%20number)
            * [find terms.pl](./oeis-research/Farideh%20Firoozbakht/Numbers%20n%20such%20that%20n+sigma(n)%20is%20a%20repunit%20number/find_terms.pl)
            * [prog.pl](./oeis-research/Farideh%20Firoozbakht/Numbers%20n%20such%20that%20n+sigma(n)%20is%20a%20repunit%20number/prog.pl)
    * [Felix Fröhlich](./oeis-research/Felix%20Fröhlich)
        * [3-powerful numbers = sum of two coprime 3-powerful numbers](./oeis-research/Felix%20Fröhlich/3-powerful%20numbers%20=%20sum%20of%20two%20coprime%203-powerful%20numbers)
            * [check.sf](./oeis-research/Felix%20Fröhlich/3-powerful%20numbers%20=%20sum%20of%20two%20coprime%203-powerful%20numbers/check.sf)
            * [generate.sf](./oeis-research/Felix%20Fröhlich/3-powerful%20numbers%20=%20sum%20of%20two%20coprime%203-powerful%20numbers/generate.sf)
            * [prog.sf](./oeis-research/Felix%20Fröhlich/3-powerful%20numbers%20=%20sum%20of%20two%20coprime%203-powerful%20numbers/prog.sf)
        * [Both truncatable primes](./oeis-research/Felix%20Fröhlich/Both%20truncatable%20primes)
            * [both truncatable primes in base.pl](./oeis-research/Felix%20Fröhlich/Both%20truncatable%20primes/both_truncatable_primes_in_base.pl)
            * [Data](./oeis-research/Felix%20Fröhlich/Both%20truncatable%20primes/data)
                * [join.pl](./oeis-research/Felix%20Fröhlich/Both%20truncatable%20primes/data/join.pl)
                * [join felix.pl](./oeis-research/Felix%20Fröhlich/Both%20truncatable%20primes/data/join_felix.pl)
            * [x.pl](./oeis-research/Felix%20Fröhlich/Both%20truncatable%20primes/x.pl)
        * [Composite k such that binomial(2k, k) = 2 that are not squares or cubes of primes](./oeis-research/Felix%20Fröhlich/Composite%20k%20such%20that%20binomial(2k,%20k)%20=%202%20that%20are%20not%20squares%20or%20cubes%20of%20primes)
            * [search.pl](./oeis-research/Felix%20Fröhlich/Composite%20k%20such%20that%20binomial(2k,%20k)%20=%202%20that%20are%20not%20squares%20or%20cubes%20of%20primes/search.pl)
        * [Felix truncatable primes](./oeis-research/Felix%20Fröhlich/Felix%20truncatable%20primes)
            * [r.pl](./oeis-research/Felix%20Fröhlich/Felix%20truncatable%20primes/r.pl)
        * [Smallest base-n Fermat pseudoprime with n distinct prime factors](./oeis-research/Felix%20Fröhlich/Smallest%20base-n%20Fermat%20pseudoprime%20with%20n%20distinct%20prime%20factors)
            * [prog.pl](./oeis-research/Felix%20Fröhlich/Smallest%20base-n%20Fermat%20pseudoprime%20with%20n%20distinct%20prime%20factors/prog.pl)
            * [prog-fast.pl](./oeis-research/Felix%20Fröhlich/Smallest%20base-n%20Fermat%20pseudoprime%20with%20n%20distinct%20prime%20factors/prog-fast.pl)
            * [prog-squarefree.pl](./oeis-research/Felix%20Fröhlich/Smallest%20base-n%20Fermat%20pseudoprime%20with%20n%20distinct%20prime%20factors/prog-squarefree.pl)
            * [prog-squarefree-fast.pl](./oeis-research/Felix%20Fröhlich/Smallest%20base-n%20Fermat%20pseudoprime%20with%20n%20distinct%20prime%20factors/prog-squarefree-fast.pl)
        * [Square array A(n, k) read by antidiagonals downwards: smallest base-n Fermat pseudoprime with k distinct prime factors for k, n >= 2](./oeis-research/Felix%20Fröhlich/Square%20array%20A(n,%20k)%20read%20by%20antidiagonals%20downwards:%20smallest%20base-n%20Fermat%20pseudoprime%20with%20k%20distinct%20prime%20factors%20for%20k,%20n%20>=%202)
            * [prog.pl](./oeis-research/Felix%20Fröhlich/Square%20array%20A(n,%20k)%20read%20by%20antidiagonals%20downwards:%20smallest%20base-n%20Fermat%20pseudoprime%20with%20k%20distinct%20prime%20factors%20for%20k,%20n%20>=%202/prog.pl)
            * [prog.sf](./oeis-research/Felix%20Fröhlich/Square%20array%20A(n,%20k)%20read%20by%20antidiagonals%20downwards:%20smallest%20base-n%20Fermat%20pseudoprime%20with%20k%20distinct%20prime%20factors%20for%20k,%20n%20>=%202/prog.sf)
    * [Felix Huber](./oeis-research/Felix%20Huber)
        * [Smallest k such that the sum of the first k primes has exactly n prime factors, counting multiplicity](./oeis-research/Felix%20Huber/Smallest%20k%20such%20that%20the%20sum%20of%20the%20first%20k%20primes%20has%20exactly%20n%20prime%20factors,%20counting%20multiplicity)
            * [prog.sf](./oeis-research/Felix%20Huber/Smallest%20k%20such%20that%20the%20sum%20of%20the%20first%20k%20primes%20has%20exactly%20n%20prime%20factors,%20counting%20multiplicity/prog.sf)
            * [prog bigint.pl](./oeis-research/Felix%20Huber/Smallest%20k%20such%20that%20the%20sum%20of%20the%20first%20k%20primes%20has%20exactly%20n%20prime%20factors,%20counting%20multiplicity/prog_bigint.pl)
            * [prog native.pl](./oeis-research/Felix%20Huber/Smallest%20k%20such%20that%20the%20sum%20of%20the%20first%20k%20primes%20has%20exactly%20n%20prime%20factors,%20counting%20multiplicity/prog_native.pl)
    * [Fernando Solanet Mayou](./oeis-research/Fernando%20Solanet%20Mayou)
        * [A(n) is the smallest number that is (zeroless) pandigital in all bases 2 <= k <= n](./oeis-research/Fernando%20Solanet%20Mayou/a(n)%20is%20the%20smallest%20number%20that%20is%20(zeroless)%20pandigital%20in%20all%20bases%202%20<=%20k%20<=%20n)
            * [prog.pl](./oeis-research/Fernando%20Solanet%20Mayou/a(n)%20is%20the%20smallest%20number%20that%20is%20(zeroless)%20pandigital%20in%20all%20bases%202%20<=%20k%20<=%20n/prog.pl)
    * [G. L. Honaker, Jr.](./oeis-research/G.%20L.%20Honaker,%20Jr.)
        * [N-pangidigital pi(n) concatenated with n](./oeis-research/G.%20L.%20Honaker,%20Jr./n-pangidigital%20pi(n)%20concatenated%20with%20n)
            * [prog.pl](./oeis-research/G.%20L.%20Honaker,%20Jr./n-pangidigital%20pi(n)%20concatenated%20with%20n/prog.pl)
        * [Numbers k such that 3 + (integer formed from first k digits after decimal point in Pi) is prime](./oeis-research/G.%20L.%20Honaker,%20Jr./Numbers%20k%20such%20that%203%20+%20(integer%20formed%20from%20first%20k%20digits%20after%20decimal%20point%20in%20Pi)%20is%20prime)
            * [search.sf](./oeis-research/G.%20L.%20Honaker,%20Jr./Numbers%20k%20such%20that%203%20+%20(integer%20formed%20from%20first%20k%20digits%20after%20decimal%20point%20in%20Pi)%20is%20prime/search.sf)
        * [Numbers n such that sigma(n) - primesigma(n) = 2*n](./oeis-research/G.%20L.%20Honaker,%20Jr./Numbers%20n%20such%20that%20sigma(n)%20-%20primesigma(n)%20=%202*n)
            * [4 primes.pl](./oeis-research/G.%20L.%20Honaker,%20Jr./Numbers%20n%20such%20that%20sigma(n)%20-%20primesigma(n)%20=%202*n/4_primes.pl)
            * [from comb.pl](./oeis-research/G.%20L.%20Honaker,%20Jr./Numbers%20n%20such%20that%20sigma(n)%20-%20primesigma(n)%20=%202*n/from_comb.pl)
            * [multi resta.pl](./oeis-research/G.%20L.%20Honaker,%20Jr./Numbers%20n%20such%20that%20sigma(n)%20-%20primesigma(n)%20=%202*n/multi_resta.pl)
            * [resta form.sf](./oeis-research/G.%20L.%20Honaker,%20Jr./Numbers%20n%20such%20that%20sigma(n)%20-%20primesigma(n)%20=%202*n/resta_form.sf)
            * [single resta.pl](./oeis-research/G.%20L.%20Honaker,%20Jr./Numbers%20n%20such%20that%20sigma(n)%20-%20primesigma(n)%20=%202*n/single_resta.pl)
            * [special form.sf](./oeis-research/G.%20L.%20Honaker,%20Jr./Numbers%20n%20such%20that%20sigma(n)%20-%20primesigma(n)%20=%202*n/special_form.sf)
    * [Gionata Neri](./oeis-research/Gionata%20Neri)
        * [Largest number k < primorial(n) such that omega(k) = n-1](./oeis-research/Gionata%20Neri/Largest%20number%20k%20<%20primorial(n)%20such%20that%20omega(k)%20=%20n-1)
            * [prog.sf](./oeis-research/Gionata%20Neri/Largest%20number%20k%20<%20primorial(n)%20such%20that%20omega(k)%20=%20n-1/prog.sf)
        * [Least number k > primorial(n) such that omega(k) = n-1](./oeis-research/Gionata%20Neri/Least%20number%20k%20>%20primorial(n)%20such%20that%20omega(k)%20=%20n-1)
            * [prog.sf](./oeis-research/Gionata%20Neri/Least%20number%20k%20>%20primorial(n)%20such%20that%20omega(k)%20=%20n-1/prog.sf)
    * [Giorgos Kalogeropoulos](./oeis-research/Giorgos%20Kalogeropoulos)
        * [Least positive integer not already in the sequence with the property that the concatenation a(0)a(1)...a(n) forms an integer with n distinct prime factors](./oeis-research/Giorgos%20Kalogeropoulos/Least%20positive%20integer%20not%20already%20in%20the%20sequence%20with%20the%20property%20that%20the%20concatenation%20a(0)a(1)...a(n)%20forms%20an%20integer%20with%20n%20distinct%20prime%20factors)
            * [prog.sf](./oeis-research/Giorgos%20Kalogeropoulos/Least%20positive%20integer%20not%20already%20in%20the%20sequence%20with%20the%20property%20that%20the%20concatenation%20a(0)a(1)...a(n)%20forms%20an%20integer%20with%20n%20distinct%20prime%20factors/prog.sf)
            * [prog 2.sf](./oeis-research/Giorgos%20Kalogeropoulos/Least%20positive%20integer%20not%20already%20in%20the%20sequence%20with%20the%20property%20that%20the%20concatenation%20a(0)a(1)...a(n)%20forms%20an%20integer%20with%20n%20distinct%20prime%20factors/prog_2.sf)
        * [Least prime p such that the n smallest primitive roots modulo p are the first n primes](./oeis-research/Giorgos%20Kalogeropoulos/Least%20prime%20p%20such%20that%20the%20n%20smallest%20primitive%20roots%20modulo%20p%20are%20the%20first%20n%20primes)
            * [prog.pl](./oeis-research/Giorgos%20Kalogeropoulos/Least%20prime%20p%20such%20that%20the%20n%20smallest%20primitive%20roots%20modulo%20p%20are%20the%20first%20n%20primes/prog.pl)
            * [upper-bounds.pl](./oeis-research/Giorgos%20Kalogeropoulos/Least%20prime%20p%20such%20that%20the%20n%20smallest%20primitive%20roots%20modulo%20p%20are%20the%20first%20n%20primes/upper-bounds.pl)
    * [Giovanni Resta](./oeis-research/Giovanni%20Resta)
        * [A(n) is the least odd number k such that Omega(k) = n and Omega(k+2) = n+1](./oeis-research/Giovanni%20Resta/a(n)%20is%20the%20least%20odd%20number%20k%20such%20that%20Omega(k)%20=%20n%20and%20Omega(k+2)%20=%20n+1)
            * [generate.pl](./oeis-research/Giovanni%20Resta/a(n)%20is%20the%20least%20odd%20number%20k%20such%20that%20Omega(k)%20=%20n%20and%20Omega(k+2)%20=%20n+1/generate.pl)
        * [Number of Carmichael numbers whose largest prime factor is prime(n)](./oeis-research/Giovanni%20Resta/Number%20of%20Carmichael%20numbers%20whose%20largest%20prime%20factor%20is%20prime(n))
            * [prog.pl](./oeis-research/Giovanni%20Resta/Number%20of%20Carmichael%20numbers%20whose%20largest%20prime%20factor%20is%20prime(n)/prog.pl)
        * [Numbers k such that k + phi(k) is a repunit](./oeis-research/Giovanni%20Resta/Numbers%20k%20such%20that%20k%20+%20phi(k)%20is%20a%20repunit)
            * [find terms.pl](./oeis-research/Giovanni%20Resta/Numbers%20k%20such%20that%20k%20+%20phi(k)%20is%20a%20repunit/find_terms.pl)
            * [prog.pl](./oeis-research/Giovanni%20Resta/Numbers%20k%20such%20that%20k%20+%20phi(k)%20is%20a%20repunit/prog.pl)
            * [semiprimes.pl](./oeis-research/Giovanni%20Resta/Numbers%20k%20such%20that%20k%20+%20phi(k)%20is%20a%20repunit/semiprimes.pl)
    * [Gonzalo Martínez](./oeis-research/Gonzalo%20Martínez)
        * [Integers k such that fib(k) + reverse(fib(k)) is prime](./oeis-research/Gonzalo%20Martínez/Integers%20k%20such%20that%20fib(k)%20+%20reverse(fib(k))%20is%20prime)
            * [prog.sf](./oeis-research/Gonzalo%20Martínez/Integers%20k%20such%20that%20fib(k)%20+%20reverse(fib(k))%20is%20prime/prog.sf)
        * [Integers k such that removing the even digits from k! yields a prime number](./oeis-research/Gonzalo%20Martínez/Integers%20k%20such%20that%20removing%20the%20even%20digits%20from%20k!%20yields%20a%20prime%20number)
            * [prog.sf](./oeis-research/Gonzalo%20Martínez/Integers%20k%20such%20that%20removing%20the%20even%20digits%20from%20k!%20yields%20a%20prime%20number/prog.sf)
    * [Greg Dresden](./oeis-research/Greg%20Dresden)
        * [Least k such that the denominators of continued fraction convergents for sqrt(k) match the first n Fibonacci numbers](./oeis-research/Greg%20Dresden/Least%20k%20such%20that%20the%20denominators%20of%20continued%20fraction%20convergents%20for%20sqrt(k)%20match%20the%20first%20n%20Fibonacci%20numbers)
            * [formula.sf](./oeis-research/Greg%20Dresden/Least%20k%20such%20that%20the%20denominators%20of%20continued%20fraction%20convergents%20for%20sqrt(k)%20match%20the%20first%20n%20Fibonacci%20numbers/formula.sf)
            * [generate.sf](./oeis-research/Greg%20Dresden/Least%20k%20such%20that%20the%20denominators%20of%20continued%20fraction%20convergents%20for%20sqrt(k)%20match%20the%20first%20n%20Fibonacci%20numbers/generate.sf)
    * [Gus Wiseman](./oeis-research/Gus%20Wiseman)
        * [Number k such that bigomega(k) * omega(k) = n](./oeis-research/Gus%20Wiseman/Number%20k%20such%20that%20bigomega(k)%20*%20omega(k)%20=%20n)
            * [search.pl](./oeis-research/Gus%20Wiseman/Number%20k%20such%20that%20bigomega(k)%20*%20omega(k)%20=%20n/search.pl)
        * [Numbers with exactly five distinct exponents in their prime factorization](./oeis-research/Gus%20Wiseman/Numbers%20with%20exactly%20five%20distinct%20exponents%20in%20their%20prime%20factorization)
            * [x.pl](./oeis-research/Gus%20Wiseman/Numbers%20with%20exactly%20five%20distinct%20exponents%20in%20their%20prime%20factorization/x.pl)
        * [Positions in A246655 (prime powers) of terms q such that there is no prime between q and the next prime power](./oeis-research/Gus%20Wiseman/Positions%20in%20A246655%20(prime%20powers)%20of%20terms%20q%20such%20that%20there%20is%20no%20prime%20between%20q%20and%20the%20next%20prime%20power)
            * [prog.sf](./oeis-research/Gus%20Wiseman/Positions%20in%20A246655%20(prime%20powers)%20of%20terms%20q%20such%20that%20there%20is%20no%20prime%20between%20q%20and%20the%20next%20prime%20power/prog.sf)
            * [prog2.sf](./oeis-research/Gus%20Wiseman/Positions%20in%20A246655%20(prime%20powers)%20of%20terms%20q%20such%20that%20there%20is%20no%20prime%20between%20q%20and%20the%20next%20prime%20power/prog2.sf)
        * [Squarefree numbers with prod(pi(p)) = 2*sum(pi(p))](./oeis-research/Gus%20Wiseman/Squarefree%20numbers%20with%20prod(pi(p))%20=%202*sum(pi(p)))
            * [prog.pl](./oeis-research/Gus%20Wiseman/Squarefree%20numbers%20with%20prod(pi(p))%20=%202*sum(pi(p))/prog.pl)
    * [Hans Havermann](./oeis-research/Hans%20Havermann)
        * [Least k such that the decimal representation of 2^k contains all possible n-digit strings](./oeis-research/Hans%20Havermann/Least%20k%20such%20that%20the%20decimal%20representation%20of%202^k%20contains%20all%20possible%20n-digit%20strings)
            * [prog.pl](./oeis-research/Hans%20Havermann/Least%20k%20such%20that%20the%20decimal%20representation%20of%202^k%20contains%20all%20possible%20n-digit%20strings/prog.pl)
            * [prog.sf](./oeis-research/Hans%20Havermann/Least%20k%20such%20that%20the%20decimal%20representation%20of%202^k%20contains%20all%20possible%20n-digit%20strings/prog.sf)
    * [Howard Berman](./oeis-research/Howard%20Berman)
        * [Numbers m such that sigma(m) is a perfect number](./oeis-research/Howard%20Berman/Numbers%20m%20such%20that%20sigma(m)%20is%20a%20perfect%20number)
            * [prog.sf](./oeis-research/Howard%20Berman/Numbers%20m%20such%20that%20sigma(m)%20is%20a%20perfect%20number/prog.sf)
    * [Hugo Pfoertner](./oeis-research/Hugo%20Pfoertner)
        * [Numbers k such that (3^k + 3*k) over 3 is prime](./oeis-research/Hugo%20Pfoertner/Numbers%20k%20such%20that%20(3^k%20+%203*k)%20over%203%20is%20prime)
            * [prog.sf](./oeis-research/Hugo%20Pfoertner/Numbers%20k%20such%20that%20(3^k%20+%203*k)%20over%203%20is%20prime/prog.sf)
        * [Numbers k such that (4^k + 4*k) over 4 is prime](./oeis-research/Hugo%20Pfoertner/Numbers%20k%20such%20that%20(4^k%20+%204*k)%20over%204%20is%20prime)
            * [prog.sf](./oeis-research/Hugo%20Pfoertner/Numbers%20k%20such%20that%20(4^k%20+%204*k)%20over%204%20is%20prime/prog.sf)
        * [Numbers k such that lucasu(3, -8, k) is prime](./oeis-research/Hugo%20Pfoertner/Numbers%20k%20such%20that%20lucasu(3,%20-8,%20k)%20is%20prime)
            * [x.pl](./oeis-research/Hugo%20Pfoertner/Numbers%20k%20such%20that%20lucasu(3,%20-8,%20k)%20is%20prime/x.pl)
        * [Numbers k such that Product {j=1..k} prime(j) + Product {j=k+1..2*k} prime(j) is prime](./oeis-research/Hugo%20Pfoertner/Numbers%20k%20such%20that%20Product_{j=1..k}%20prime(j)%20+%20Product_{j=k+1..2*k}%20prime(j)%20is%20prime)
            * [prog.sf](./oeis-research/Hugo%20Pfoertner/Numbers%20k%20such%20that%20Product_{j=1..k}%20prime(j)%20+%20Product_{j=k+1..2*k}%20prime(j)%20is%20prime/prog.sf)
        * [Numbers n such that 2^n + n + 2 is prime](./oeis-research/Hugo%20Pfoertner/Numbers%20n%20such%20that%202^n%20+%20n%20+%202%20is%20prime)
            * [prog.sf](./oeis-research/Hugo%20Pfoertner/Numbers%20n%20such%20that%202^n%20+%20n%20+%202%20is%20prime/prog.sf)
        * [Numbers n such that n^(n + 1) + n - 1 is prime](./oeis-research/Hugo%20Pfoertner/Numbers%20n%20such%20that%20n^(n%20+%201)%20+%20n%20-%201%20is%20prime)
            * [prog.sf](./oeis-research/Hugo%20Pfoertner/Numbers%20n%20such%20that%20n^(n%20+%201)%20+%20n%20-%201%20is%20prime/prog.sf)
        * [Numbers n such that n^4 + 4^n is a semiprime](./oeis-research/Hugo%20Pfoertner/Numbers%20n%20such%20that%20n^4%20+%204^n%20is%20a%20semiprime)
            * [prog.pl](./oeis-research/Hugo%20Pfoertner/Numbers%20n%20such%20that%20n^4%20+%204^n%20is%20a%20semiprime/prog.pl)
    * [Ilya Gutkovskiy](./oeis-research/Ilya%20Gutkovskiy)
        * [A(n) is the index of the smallest square pyramidal number divisible by exactly n square pyramidal numbers](./oeis-research/Ilya%20Gutkovskiy/a(n)%20is%20the%20index%20of%20the%20smallest%20square%20pyramidal%20number%20divisible%20by%20exactly%20n%20square%20pyramidal%20numbers)
            * [prog.pl](./oeis-research/Ilya%20Gutkovskiy/a(n)%20is%20the%20index%20of%20the%20smallest%20square%20pyramidal%20number%20divisible%20by%20exactly%20n%20square%20pyramidal%20numbers/prog.pl)
            * [prog.sf](./oeis-research/Ilya%20Gutkovskiy/a(n)%20is%20the%20index%20of%20the%20smallest%20square%20pyramidal%20number%20divisible%20by%20exactly%20n%20square%20pyramidal%20numbers/prog.sf)
        * [Consecutive integers with equal bigomega(n) - omega(n)](./oeis-research/Ilya%20Gutkovskiy/Consecutive%20integers%20with%20equal%20bigomega(n)%20-%20omega(n))
            * [find a(8).pl](./oeis-research/Ilya%20Gutkovskiy/Consecutive%20integers%20with%20equal%20bigomega(n)%20-%20omega(n)/find_a(8).pl)
            * [prog.pl](./oeis-research/Ilya%20Gutkovskiy/Consecutive%20integers%20with%20equal%20bigomega(n)%20-%20omega(n)/prog.pl)
            * [prog.sf](./oeis-research/Ilya%20Gutkovskiy/Consecutive%20integers%20with%20equal%20bigomega(n)%20-%20omega(n)/prog.sf)
            * [smooth generate.pl](./oeis-research/Ilya%20Gutkovskiy/Consecutive%20integers%20with%20equal%20bigomega(n)%20-%20omega(n)/smooth_generate.pl)
        * [Consecutive integers with equal sigma0(n) - omega(n)](./oeis-research/Ilya%20Gutkovskiy/Consecutive%20integers%20with%20equal%20sigma0(n)%20-%20omega(n))
            * [find a(10).pl](./oeis-research/Ilya%20Gutkovskiy/Consecutive%20integers%20with%20equal%20sigma0(n)%20-%20omega(n)/find_a(10).pl)
            * [prog.pl](./oeis-research/Ilya%20Gutkovskiy/Consecutive%20integers%20with%20equal%20sigma0(n)%20-%20omega(n)/prog.pl)
        * [Index of the smallest Fibonacci n-step number with exactly n distinct prime factors](./oeis-research/Ilya%20Gutkovskiy/Index%20of%20the%20smallest%20Fibonacci%20n-step%20number%20with%20exactly%20n%20distinct%20prime%20factors)
            * [prog.sf](./oeis-research/Ilya%20Gutkovskiy/Index%20of%20the%20smallest%20Fibonacci%20n-step%20number%20with%20exactly%20n%20distinct%20prime%20factors/prog.sf)
        * [Index of the smallest Fibonacci n-step number with exactly n prime factors (counted with multiplicity)](./oeis-research/Ilya%20Gutkovskiy/Index%20of%20the%20smallest%20Fibonacci%20n-step%20number%20with%20exactly%20n%20prime%20factors%20(counted%20with%20multiplicity))
            * [prog.sf](./oeis-research/Ilya%20Gutkovskiy/Index%20of%20the%20smallest%20Fibonacci%20n-step%20number%20with%20exactly%20n%20prime%20factors%20(counted%20with%20multiplicity)/prog.sf)
        * [Index of the smallest n-gonal number divisible by exactly n n-gonal numbers](./oeis-research/Ilya%20Gutkovskiy/Index%20of%20the%20smallest%20n-gonal%20number%20divisible%20by%20exactly%20n%20n-gonal%20numbers)
            * [prog.pl](./oeis-research/Ilya%20Gutkovskiy/Index%20of%20the%20smallest%20n-gonal%20number%20divisible%20by%20exactly%20n%20n-gonal%20numbers/prog.pl)
            * [prog 2.pl](./oeis-research/Ilya%20Gutkovskiy/Index%20of%20the%20smallest%20n-gonal%20number%20divisible%20by%20exactly%20n%20n-gonal%20numbers/prog_2.pl)
        * [Index of the smallest n-gonal pyramidal number divisible by exactly n n-gonal pyramidal numbers](./oeis-research/Ilya%20Gutkovskiy/Index%20of%20the%20smallest%20n-gonal%20pyramidal%20number%20divisible%20by%20exactly%20n%20n-gonal%20pyramidal%20numbers)
            * [prog.pl](./oeis-research/Ilya%20Gutkovskiy/Index%20of%20the%20smallest%20n-gonal%20pyramidal%20number%20divisible%20by%20exactly%20n%20n-gonal%20pyramidal%20numbers/prog.pl)
        * [Index of the smallest square pyramidal number with exactly n prime factors (counted with multiplicity)](./oeis-research/Ilya%20Gutkovskiy/Index%20of%20the%20smallest%20square%20pyramidal%20number%20with%20exactly%20n%20prime%20factors%20(counted%20with%20multiplicity))
            * [prog.sf](./oeis-research/Ilya%20Gutkovskiy/Index%20of%20the%20smallest%20square%20pyramidal%20number%20with%20exactly%20n%20prime%20factors%20(counted%20with%20multiplicity)/prog.sf)
        * [Index of the smallest tetrahedral number with exactly n distinct prime factors](./oeis-research/Ilya%20Gutkovskiy/Index%20of%20the%20smallest%20tetrahedral%20number%20with%20exactly%20n%20distinct%20prime%20factors)
            * [prog.pl](./oeis-research/Ilya%20Gutkovskiy/Index%20of%20the%20smallest%20tetrahedral%20number%20with%20exactly%20n%20distinct%20prime%20factors/prog.pl)
            * [prog.sf](./oeis-research/Ilya%20Gutkovskiy/Index%20of%20the%20smallest%20tetrahedral%20number%20with%20exactly%20n%20distinct%20prime%20factors/prog.sf)
        * [Index of the smallest tetrahedral number with exactly n prime factors (counted with multiplicity), or -1 if no such number exists](./oeis-research/Ilya%20Gutkovskiy/Index%20of%20the%20smallest%20tetrahedral%20number%20with%20exactly%20n%20prime%20factors%20(counted%20with%20multiplicity),%20or%20-1%20if%20no%20such%20number%20exists)
            * [prog.pl](./oeis-research/Ilya%20Gutkovskiy/Index%20of%20the%20smallest%20tetrahedral%20number%20with%20exactly%20n%20prime%20factors%20(counted%20with%20multiplicity),%20or%20-1%20if%20no%20such%20number%20exists/prog.pl)
            * [prog.sf](./oeis-research/Ilya%20Gutkovskiy/Index%20of%20the%20smallest%20tetrahedral%20number%20with%20exactly%20n%20prime%20factors%20(counted%20with%20multiplicity),%20or%20-1%20if%20no%20such%20number%20exists/prog.sf)
            * [prog 2.pl](./oeis-research/Ilya%20Gutkovskiy/Index%20of%20the%20smallest%20tetrahedral%20number%20with%20exactly%20n%20prime%20factors%20(counted%20with%20multiplicity),%20or%20-1%20if%20no%20such%20number%20exists/prog_2.pl)
        * [Index of the smallest tetranacci number (A000078) with exactly n distinct prime factors](./oeis-research/Ilya%20Gutkovskiy/Index%20of%20the%20smallest%20tetranacci%20number%20(A000078)%20with%20exactly%20n%20distinct%20prime%20factors)
            * [prog.sf](./oeis-research/Ilya%20Gutkovskiy/Index%20of%20the%20smallest%20tetranacci%20number%20(A000078)%20with%20exactly%20n%20distinct%20prime%20factors/prog.sf)
        * [Index of the smallest tetranacci number (A000078) with exactly n prime factors (counted with multiplicity)](./oeis-research/Ilya%20Gutkovskiy/Index%20of%20the%20smallest%20tetranacci%20number%20(A000078)%20with%20exactly%20n%20prime%20factors%20(counted%20with%20multiplicity))
            * [prog.sf](./oeis-research/Ilya%20Gutkovskiy/Index%20of%20the%20smallest%20tetranacci%20number%20(A000078)%20with%20exactly%20n%20prime%20factors%20(counted%20with%20multiplicity)/prog.sf)
        * [Index of the smallest tribonacci number (A000073) with exactly n distinct prime factors](./oeis-research/Ilya%20Gutkovskiy/Index%20of%20the%20smallest%20tribonacci%20number%20(A000073)%20with%20exactly%20n%20distinct%20prime%20factors)
            * [prog.sf](./oeis-research/Ilya%20Gutkovskiy/Index%20of%20the%20smallest%20tribonacci%20number%20(A000073)%20with%20exactly%20n%20distinct%20prime%20factors/prog.sf)
        * [Index of the smallest tribonacci number (A000073) with exactly n prime factors (counted with multiplicity)](./oeis-research/Ilya%20Gutkovskiy/Index%20of%20the%20smallest%20tribonacci%20number%20(A000073)%20with%20exactly%20n%20prime%20factors%20(counted%20with%20multiplicity))
            * [prog.sf](./oeis-research/Ilya%20Gutkovskiy/Index%20of%20the%20smallest%20tribonacci%20number%20(A000073)%20with%20exactly%20n%20prime%20factors%20(counted%20with%20multiplicity)/prog.sf)
        * [Least number k such that the average number of prime divisors of {1..k} counted with multiplicity is >= n](./oeis-research/Ilya%20Gutkovskiy/Least%20number%20k%20such%20that%20the%20average%20number%20of%20prime%20divisors%20of%20{1..k}%20counted%20with%20multiplicity%20is%20>=%20n)
            * [prog.pl](./oeis-research/Ilya%20Gutkovskiy/Least%20number%20k%20such%20that%20the%20average%20number%20of%20prime%20divisors%20of%20{1..k}%20counted%20with%20multiplicity%20is%20>=%20n/prog.pl)
        * [Maximal coefficient of (1 + x^a(1)) * (1 + x^a(1) + x^a(2)) * ... * (1 + x^a(1) + x^a(2) + ... + x^a(n-1))](./oeis-research/Ilya%20Gutkovskiy/Maximal%20coefficient%20of%20(1%20+%20x^a(1))%20*%20(1%20+%20x^a(1)%20+%20x^a(2))%20*%20...%20*%20(1%20+%20x^a(1)%20+%20x^a(2)%20+%20...%20+%20x^a(n-1)))
            * [prog.sf](./oeis-research/Ilya%20Gutkovskiy/Maximal%20coefficient%20of%20(1%20+%20x^a(1))%20*%20(1%20+%20x^a(1)%20+%20x^a(2))%20*%20...%20*%20(1%20+%20x^a(1)%20+%20x^a(2)%20+%20...%20+%20x^a(n-1))/prog.sf)
        * [N-th prime recursive sum](./oeis-research/Ilya%20Gutkovskiy/N-th%20prime%20recursive%20sum)
            * [prog.sf](./oeis-research/Ilya%20Gutkovskiy/N-th%20prime%20recursive%20sum/prog.sf)
        * [Number of subsets of {1..n} whose harmonic mean is an integer](./oeis-research/Ilya%20Gutkovskiy/Number%20of%20subsets%20of%20{1..n}%20whose%20harmonic%20mean%20is%20an%20integer)
            * [prog.sf](./oeis-research/Ilya%20Gutkovskiy/Number%20of%20subsets%20of%20{1..n}%20whose%20harmonic%20mean%20is%20an%20integer/prog.sf)
        * [Numbers k such that the average number of odd divisors of {1..k} is an integer](./oeis-research/Ilya%20Gutkovskiy/Numbers%20k%20such%20that%20the%20average%20number%20of%20odd%20divisors%20of%20{1..k}%20is%20an%20integer)
            * [binary search.sf](./oeis-research/Ilya%20Gutkovskiy/Numbers%20k%20such%20that%20the%20average%20number%20of%20odd%20divisors%20of%20{1..k}%20is%20an%20integer/binary_search.sf)
        * [Perfect powers that are equal to the sum of the first k perfect powers > 1 for some k](./oeis-research/Ilya%20Gutkovskiy/Perfect%20powers%20that%20are%20equal%20to%20the%20sum%20of%20the%20first%20k%20perfect%20powers%20>%201%20for%20some%20k)
            * [prog.sf](./oeis-research/Ilya%20Gutkovskiy/Perfect%20powers%20that%20are%20equal%20to%20the%20sum%20of%20the%20first%20k%20perfect%20powers%20>%201%20for%20some%20k/prog.sf)
        * [Smallest centered n-gonal number divisible by exactly n centered n-gonal numbers](./oeis-research/Ilya%20Gutkovskiy/Smallest%20centered%20n-gonal%20number%20divisible%20by%20exactly%20n%20centered%20n-gonal%20numbers)
            * [prog.pl](./oeis-research/Ilya%20Gutkovskiy/Smallest%20centered%20n-gonal%20number%20divisible%20by%20exactly%20n%20centered%20n-gonal%20numbers/prog.pl)
        * [Smallest centered n-gonal number with exactly n distinct prime factors](./oeis-research/Ilya%20Gutkovskiy/Smallest%20centered%20n-gonal%20number%20with%20exactly%20n%20distinct%20prime%20factors)
            * [omega primes.sf](./oeis-research/Ilya%20Gutkovskiy/Smallest%20centered%20n-gonal%20number%20with%20exactly%20n%20distinct%20prime%20factors/omega_primes.sf)
            * [prog.pl](./oeis-research/Ilya%20Gutkovskiy/Smallest%20centered%20n-gonal%20number%20with%20exactly%20n%20distinct%20prime%20factors/prog.pl)
            * [prog.sf](./oeis-research/Ilya%20Gutkovskiy/Smallest%20centered%20n-gonal%20number%20with%20exactly%20n%20distinct%20prime%20factors/prog.sf)
        * [Smallest centered n-gonal number with exactly n prime factors (counted with multiplicity)](./oeis-research/Ilya%20Gutkovskiy/Smallest%20centered%20n-gonal%20number%20with%20exactly%20n%20prime%20factors%20(counted%20with%20multiplicity))
            * [almost primes.sf](./oeis-research/Ilya%20Gutkovskiy/Smallest%20centered%20n-gonal%20number%20with%20exactly%20n%20prime%20factors%20(counted%20with%20multiplicity)/almost_primes.sf)
            * [prog.pl](./oeis-research/Ilya%20Gutkovskiy/Smallest%20centered%20n-gonal%20number%20with%20exactly%20n%20prime%20factors%20(counted%20with%20multiplicity)/prog.pl)
        * [Smallest centered square number divisible by exactly n centered square numbers](./oeis-research/Ilya%20Gutkovskiy/Smallest%20centered%20square%20number%20divisible%20by%20exactly%20n%20centered%20square%20numbers)
            * [prog.pl](./oeis-research/Ilya%20Gutkovskiy/Smallest%20centered%20square%20number%20divisible%20by%20exactly%20n%20centered%20square%20numbers/prog.pl)
        * [Smallest centered square number with exactly n distinct prime factors](./oeis-research/Ilya%20Gutkovskiy/Smallest%20centered%20square%20number%20with%20exactly%20n%20distinct%20prime%20factors)
            * [prog.pl](./oeis-research/Ilya%20Gutkovskiy/Smallest%20centered%20square%20number%20with%20exactly%20n%20distinct%20prime%20factors/prog.pl)
        * [Smallest centered square number with exactly n prime factors (counted with multiplicity)](./oeis-research/Ilya%20Gutkovskiy/Smallest%20centered%20square%20number%20with%20exactly%20n%20prime%20factors%20(counted%20with%20multiplicity))
            * [almost primes.sf](./oeis-research/Ilya%20Gutkovskiy/Smallest%20centered%20square%20number%20with%20exactly%20n%20prime%20factors%20(counted%20with%20multiplicity)/almost_primes.sf)
            * [prog.pl](./oeis-research/Ilya%20Gutkovskiy/Smallest%20centered%20square%20number%20with%20exactly%20n%20prime%20factors%20(counted%20with%20multiplicity)/prog.pl)
        * [Smallest centered triangular number with exactly n distinct prime factors](./oeis-research/Ilya%20Gutkovskiy/Smallest%20centered%20triangular%20number%20with%20exactly%20n%20distinct%20prime%20factors)
            * [prog.pl](./oeis-research/Ilya%20Gutkovskiy/Smallest%20centered%20triangular%20number%20with%20exactly%20n%20distinct%20prime%20factors/prog.pl)
        * [Smallest centered triangular number with exactly n prime factors (counted with multiplicity)](./oeis-research/Ilya%20Gutkovskiy/Smallest%20centered%20triangular%20number%20with%20exactly%20n%20prime%20factors%20(counted%20with%20multiplicity))
            * [prog.pl](./oeis-research/Ilya%20Gutkovskiy/Smallest%20centered%20triangular%20number%20with%20exactly%20n%20prime%20factors%20(counted%20with%20multiplicity)/prog.pl)
        * [Smallest n-gonal number divisible by exactly n n-gonal numbers](./oeis-research/Ilya%20Gutkovskiy/Smallest%20n-gonal%20number%20divisible%20by%20exactly%20n%20n-gonal%20numbers)
            * [prog.pl](./oeis-research/Ilya%20Gutkovskiy/Smallest%20n-gonal%20number%20divisible%20by%20exactly%20n%20n-gonal%20numbers/prog.pl)
        * [Smallest n-gonal number with exactly n distinct prime factors](./oeis-research/Ilya%20Gutkovskiy/Smallest%20n-gonal%20number%20with%20exactly%20n%20distinct%20prime%20factors)
            * [omega primes.sf](./oeis-research/Ilya%20Gutkovskiy/Smallest%20n-gonal%20number%20with%20exactly%20n%20distinct%20prime%20factors/omega_primes.sf)
            * [prog.pl](./oeis-research/Ilya%20Gutkovskiy/Smallest%20n-gonal%20number%20with%20exactly%20n%20distinct%20prime%20factors/prog.pl)
        * [Smallest n-gonal number with exactly n prime factors (counted with multiplicity)](./oeis-research/Ilya%20Gutkovskiy/Smallest%20n-gonal%20number%20with%20exactly%20n%20prime%20factors%20(counted%20with%20multiplicity))
            * [almost primes.sf](./oeis-research/Ilya%20Gutkovskiy/Smallest%20n-gonal%20number%20with%20exactly%20n%20prime%20factors%20(counted%20with%20multiplicity)/almost_primes.sf)
            * [prog.pl](./oeis-research/Ilya%20Gutkovskiy/Smallest%20n-gonal%20number%20with%20exactly%20n%20prime%20factors%20(counted%20with%20multiplicity)/prog.pl)
        * [Smallest n-gonal pyramidal number divisible by exactly n n-gonal pyramidal numbers](./oeis-research/Ilya%20Gutkovskiy/Smallest%20n-gonal%20pyramidal%20number%20divisible%20by%20exactly%20n%20n-gonal%20pyramidal%20numbers)
            * [prog.pl](./oeis-research/Ilya%20Gutkovskiy/Smallest%20n-gonal%20pyramidal%20number%20divisible%20by%20exactly%20n%20n-gonal%20pyramidal%20numbers/prog.pl)
            * [prog.sf](./oeis-research/Ilya%20Gutkovskiy/Smallest%20n-gonal%20pyramidal%20number%20divisible%20by%20exactly%20n%20n-gonal%20pyramidal%20numbers/prog.sf)
            * [prog 2.pl](./oeis-research/Ilya%20Gutkovskiy/Smallest%20n-gonal%20pyramidal%20number%20divisible%20by%20exactly%20n%20n-gonal%20pyramidal%20numbers/prog_2.pl)
        * [Smallest n-gonal pyramidal number which can be represented as the sum of n distinct nonzero n-gonal pyramidal numbers in exactly n ways, or -1 if none exists](./oeis-research/Ilya%20Gutkovskiy/Smallest%20n-gonal%20pyramidal%20number%20which%20can%20be%20represented%20as%20the%20sum%20of%20n%20distinct%20nonzero%20n-gonal%20pyramidal%20numbers%20in%20exactly%20n%20ways,%20or%20-1%20if%20none%20exists)
            * [prog.sf](./oeis-research/Ilya%20Gutkovskiy/Smallest%20n-gonal%20pyramidal%20number%20which%20can%20be%20represented%20as%20the%20sum%20of%20n%20distinct%20nonzero%20n-gonal%20pyramidal%20numbers%20in%20exactly%20n%20ways,%20or%20-1%20if%20none%20exists/prog.sf)
        * [Smallest n-gonal pyramidal number with exactly n distinct prime factors](./oeis-research/Ilya%20Gutkovskiy/Smallest%20n-gonal%20pyramidal%20number%20with%20exactly%20n%20distinct%20prime%20factors)
            * [prog.sf](./oeis-research/Ilya%20Gutkovskiy/Smallest%20n-gonal%20pyramidal%20number%20with%20exactly%20n%20distinct%20prime%20factors/prog.sf)
        * [Smallest n-gonal pyramidal number with exactly n prime factors (counted with multiplicity)](./oeis-research/Ilya%20Gutkovskiy/Smallest%20n-gonal%20pyramidal%20number%20with%20exactly%20n%20prime%20factors%20(counted%20with%20multiplicity))
            * [prog.sf](./oeis-research/Ilya%20Gutkovskiy/Smallest%20n-gonal%20pyramidal%20number%20with%20exactly%20n%20prime%20factors%20(counted%20with%20multiplicity)/prog.sf)
        * [Smallest number k such that n consecutive integers starting at k have the same number of triangular divisors](./oeis-research/Ilya%20Gutkovskiy/Smallest%20number%20k%20such%20that%20n%20consecutive%20integers%20starting%20at%20k%20have%20the%20same%20number%20of%20triangular%20divisors)
            * [prog.pl](./oeis-research/Ilya%20Gutkovskiy/Smallest%20number%20k%20such%20that%20n%20consecutive%20integers%20starting%20at%20k%20have%20the%20same%20number%20of%20triangular%20divisors/prog.pl)
        * [Smallest number that is the sum of two distinct n-th powers of primes in two different ways](./oeis-research/Ilya%20Gutkovskiy/Smallest%20number%20that%20is%20the%20sum%20of%20two%20distinct%20n-th%20powers%20of%20primes%20in%20two%20different%20ways)
            * [search.jl](./oeis-research/Ilya%20Gutkovskiy/Smallest%20number%20that%20is%20the%20sum%20of%20two%20distinct%20n-th%20powers%20of%20primes%20in%20two%20different%20ways/search.jl)
        * [Smallest number which can be represented as the product of n distinct integers > 1 in exactly n ways](./oeis-research/Ilya%20Gutkovskiy/Smallest%20number%20which%20can%20be%20represented%20as%20the%20product%20of%20n%20distinct%20integers%20>%201%20in%20exactly%20n%20ways)
            * [prog.pl](./oeis-research/Ilya%20Gutkovskiy/Smallest%20number%20which%20can%20be%20represented%20as%20the%20product%20of%20n%20distinct%20integers%20>%201%20in%20exactly%20n%20ways/prog.pl)
            * [prog.sf](./oeis-research/Ilya%20Gutkovskiy/Smallest%20number%20which%20can%20be%20represented%20as%20the%20product%20of%20n%20distinct%20integers%20>%201%20in%20exactly%20n%20ways/prog.sf)
            * [prog slow.sf](./oeis-research/Ilya%20Gutkovskiy/Smallest%20number%20which%20can%20be%20represented%20as%20the%20product%20of%20n%20distinct%20integers%20>%201%20in%20exactly%20n%20ways/prog_slow.sf)
        * [Smallest number with exactly n divisors that are n-gonal numbers](./oeis-research/Ilya%20Gutkovskiy/Smallest%20number%20with%20exactly%20n%20divisors%20that%20are%20n-gonal%20numbers)
            * [prog.pl](./oeis-research/Ilya%20Gutkovskiy/Smallest%20number%20with%20exactly%20n%20divisors%20that%20are%20n-gonal%20numbers/prog.pl)
        * [Smallest positive integer which can be represented as the sum of distinct positive Fibonacci n-step numbers (with a single type of 1) in exactly n ways, or -1 if no such integer exists](./oeis-research/Ilya%20Gutkovskiy/Smallest%20positive%20integer%20which%20can%20be%20represented%20as%20the%20sum%20of%20distinct%20positive%20Fibonacci%20n-step%20numbers%20(with%20a%20single%20type%20of%201)%20in%20exactly%20n%20ways,%20or%20-1%20if%20no%20such%20integer%20exists)
            * [prog.sf](./oeis-research/Ilya%20Gutkovskiy/Smallest%20positive%20integer%20which%20can%20be%20represented%20as%20the%20sum%20of%20distinct%20positive%20Fibonacci%20n-step%20numbers%20(with%20a%20single%20type%20of%201)%20in%20exactly%20n%20ways,%20or%20-1%20if%20no%20such%20integer%20exists/prog.sf)
        * [Smallest square pyramidal number with exactly n distinct prime factors](./oeis-research/Ilya%20Gutkovskiy/Smallest%20square%20pyramidal%20number%20with%20exactly%20n%20distinct%20prime%20factors)
            * [prog.sf](./oeis-research/Ilya%20Gutkovskiy/Smallest%20square%20pyramidal%20number%20with%20exactly%20n%20distinct%20prime%20factors/prog.sf)
        * [Squarefree harmonic sum exceeds n](./oeis-research/Ilya%20Gutkovskiy/Squarefree%20harmonic%20sum%20exceeds%20n)
            * [prog.pl](./oeis-research/Ilya%20Gutkovskiy/Squarefree%20harmonic%20sum%20exceeds%20n/prog.pl)
    * [Irina Gerasimova](./oeis-research/Irina%20Gerasimova)
        * [Numbers n such that Omega(n) = Omega(2^n + 1), where Omega = A001222 is the number of prime factors counted with multiplicity](./oeis-research/Irina%20Gerasimova/Numbers%20n%20such%20that%20Omega(n)%20=%20Omega(2^n%20+%201),%20where%20Omega%20=%20A001222%20is%20the%20number%20of%20prime%20factors%20counted%20with%20multiplicity)
            * [prog.sf](./oeis-research/Irina%20Gerasimova/Numbers%20n%20such%20that%20Omega(n)%20=%20Omega(2^n%20+%201),%20where%20Omega%20=%20A001222%20is%20the%20number%20of%20prime%20factors%20counted%20with%20multiplicity/prog.sf)
    * [Ivan N. Ianakiev](./oeis-research/Ivan%20N.%20Ianakiev)
        * [Intersection of A000330 and A086849](./oeis-research/Ivan%20N.%20Ianakiev/Intersection%20of%20A000330%20and%20A086849)
            * [prog.pl](./oeis-research/Ivan%20N.%20Ianakiev/Intersection%20of%20A000330%20and%20A086849/prog.pl)
            * [prog.sf](./oeis-research/Ivan%20N.%20Ianakiev/Intersection%20of%20A000330%20and%20A086849/prog.sf)
    * [J. Lowell](./oeis-research/J.%20Lowell)
        * [A(1)=1; for n > 1, a(n) is the smallest number with the same number of divisors as 2*a(n-1)](./oeis-research/J.%20Lowell/a(1)=1;%20for%20n%20>%201,%20a(n)%20is%20the%20smallest%20number%20with%20the%20same%20number%20of%20divisors%20as%202*a(n-1))
            * [prog.pl](./oeis-research/J.%20Lowell/a(1)=1;%20for%20n%20>%201,%20a(n)%20is%20the%20smallest%20number%20with%20the%20same%20number%20of%20divisors%20as%202*a(n-1)/prog.pl)
        * [A(1)=2048. For n>1, a(n) is the LCM of a(n-1) and A140635(a(n-1))](./oeis-research/J.%20Lowell/a(1)=2048.%20For%20n>1,%20a(n)%20is%20the%20LCM%20of%20a(n-1)%20and%20A140635(a(n-1)))
            * [prog.pl](./oeis-research/J.%20Lowell/a(1)=2048.%20For%20n>1,%20a(n)%20is%20the%20LCM%20of%20a(n-1)%20and%20A140635(a(n-1))/prog.pl)
    * [J. M. Bergot](./oeis-research/J.%20M.%20Bergot)
        * [A(n) is the first number k with A340967(k) = n](./oeis-research/J.%20M.%20Bergot/a(n)%20is%20the%20first%20number%20k%20with%20A340967(k)%20=%20n)
            * [prog.pl](./oeis-research/J.%20M.%20Bergot/a(n)%20is%20the%20first%20number%20k%20with%20A340967(k)%20=%20n/prog.pl)
        * [A(n) is the first prime p such that, with q the next prime, p + q^2 is 10^n times a prime](./oeis-research/J.%20M.%20Bergot/a(n)%20is%20the%20first%20prime%20p%20such%20that,%20with%20q%20the%20next%20prime,%20p%20+%20q^2%20is%2010^n%20times%20a%20prime)
            * [equation solutions.sf](./oeis-research/J.%20M.%20Bergot/a(n)%20is%20the%20first%20prime%20p%20such%20that,%20with%20q%20the%20next%20prime,%20p%20+%20q^2%20is%2010^n%20times%20a%20prime/equation_solutions.sf)
            * [prog.pl](./oeis-research/J.%20M.%20Bergot/a(n)%20is%20the%20first%20prime%20p%20such%20that,%20with%20q%20the%20next%20prime,%20p%20+%20q^2%20is%2010^n%20times%20a%20prime/prog.pl)
            * [upper-bounds.sf](./oeis-research/J.%20M.%20Bergot/a(n)%20is%20the%20first%20prime%20p%20such%20that,%20with%20q%20the%20next%20prime,%20p%20+%20q^2%20is%2010^n%20times%20a%20prime/upper-bounds.sf)
        * [A(n) is the first prime p such that, with q the next prime, p^2+q is 10^n times a prime](./oeis-research/J.%20M.%20Bergot/a(n)%20is%20the%20first%20prime%20p%20such%20that,%20with%20q%20the%20next%20prime,%20p^2+q%20is%2010^n%20times%20a%20prime)
            * [equation solutions.sf](./oeis-research/J.%20M.%20Bergot/a(n)%20is%20the%20first%20prime%20p%20such%20that,%20with%20q%20the%20next%20prime,%20p^2+q%20is%2010^n%20times%20a%20prime/equation_solutions.sf)
            * [larger terms from known terms.sf](./oeis-research/J.%20M.%20Bergot/a(n)%20is%20the%20first%20prime%20p%20such%20that,%20with%20q%20the%20next%20prime,%20p^2+q%20is%2010^n%20times%20a%20prime/larger_terms_from_known_terms.sf)
            * [prog.pl](./oeis-research/J.%20M.%20Bergot/a(n)%20is%20the%20first%20prime%20p%20such%20that,%20with%20q%20the%20next%20prime,%20p^2+q%20is%2010^n%20times%20a%20prime/prog.pl)
            * [upper bounds.sf](./oeis-research/J.%20M.%20Bergot/a(n)%20is%20the%20first%20prime%20p%20such%20that,%20with%20q%20the%20next%20prime,%20p^2+q%20is%2010^n%20times%20a%20prime/upper_bounds.sf)
        * [A(n) is the first prime that is the start of a sequence of exactly n primes under the map p -> p + sopfr(p-1) + sopfr(p+1)](./oeis-research/J.%20M.%20Bergot/a(n)%20is%20the%20first%20prime%20that%20is%20the%20start%20of%20a%20sequence%20of%20exactly%20n%20primes%20under%20the%20map%20p%20->%20p%20+%20sopfr(p-1)%20+%20sopfr(p+1))
            * [prog.pl](./oeis-research/J.%20M.%20Bergot/a(n)%20is%20the%20first%20prime%20that%20is%20the%20start%20of%20a%20sequence%20of%20exactly%20n%20primes%20under%20the%20map%20p%20->%20p%20+%20sopfr(p-1)%20+%20sopfr(p+1)/prog.pl)
        * [A(n) is the first prime that starts a sequence of exactly n consecutive primes prime(k+1), ..., prime(k+n) where prime(k+i)+2^i is prime for i = 1...n but not for i = n+1](./oeis-research/J.%20M.%20Bergot/a(n)%20is%20the%20first%20prime%20that%20starts%20a%20sequence%20of%20exactly%20n%20consecutive%20primes%20prime(k+1),%20...,%20prime(k+n)%20where%20prime(k+i)+2^i%20is%20prime%20for%20i%20=%201...n%20but%20not%20for%20i%20=%20n+1)
            * [prog.pl](./oeis-research/J.%20M.%20Bergot/a(n)%20is%20the%20first%20prime%20that%20starts%20a%20sequence%20of%20exactly%20n%20consecutive%20primes%20prime(k+1),%20...,%20prime(k+n)%20where%20prime(k+i)+2^i%20is%20prime%20for%20i%20=%201...n%20but%20not%20for%20i%20=%20n+1/prog.pl)
            * [upper-bounds.pl](./oeis-research/J.%20M.%20Bergot/a(n)%20is%20the%20first%20prime%20that%20starts%20a%20sequence%20of%20exactly%20n%20consecutive%20primes%20prime(k+1),%20...,%20prime(k+n)%20where%20prime(k+i)+2^i%20is%20prime%20for%20i%20=%201...n%20but%20not%20for%20i%20=%20n+1/upper-bounds.pl)
        * [A(n) is the first prime that starts a string of exactly n consecutive primes that are in A347702](./oeis-research/J.%20M.%20Bergot/a(n)%20is%20the%20first%20prime%20that%20starts%20a%20string%20of%20exactly%20n%20consecutive%20primes%20that%20are%20in%20A347702)
            * [prog.pl](./oeis-research/J.%20M.%20Bergot/a(n)%20is%20the%20first%20prime%20that%20starts%20a%20string%20of%20exactly%20n%20consecutive%20primes%20that%20are%20in%20A347702/prog.pl)
        * [A(n) is the least k such that bigomega(k)=n and bigomega(k+1)=n+1](./oeis-research/J.%20M.%20Bergot/a(n)%20is%20the%20least%20k%20such%20that%20bigomega(k)=n%20and%20bigomega(k+1)=n+1)
            * [generate.pl](./oeis-research/J.%20M.%20Bergot/a(n)%20is%20the%20least%20k%20such%20that%20bigomega(k)=n%20and%20bigomega(k+1)=n+1/generate.pl)
            * [prog faster.pl](./oeis-research/J.%20M.%20Bergot/a(n)%20is%20the%20least%20k%20such%20that%20bigomega(k)=n%20and%20bigomega(k+1)=n+1/prog_faster.pl)
            * [prog low memory.pl](./oeis-research/J.%20M.%20Bergot/a(n)%20is%20the%20least%20k%20such%20that%20bigomega(k)=n%20and%20bigomega(k+1)=n+1/prog_low_memory.pl)
        * [A(n) is the least prime p such that bigomega(p+n) = bigomega(p-n) = n](./oeis-research/J.%20M.%20Bergot/a(n)%20is%20the%20least%20prime%20p%20such%20that%20bigomega(p+n)%20=%20bigomega(p-n)%20=%20n)
            * [upper-bounds.pl](./oeis-research/J.%20M.%20Bergot/a(n)%20is%20the%20least%20prime%20p%20such%20that%20bigomega(p+n)%20=%20bigomega(p-n)%20=%20n/upper-bounds.pl)
            * [upper-bounds.sf](./oeis-research/J.%20M.%20Bergot/a(n)%20is%20the%20least%20prime%20p%20such%20that%20bigomega(p+n)%20=%20bigomega(p-n)%20=%20n/upper-bounds.sf)
        * [A(n) is the least prime p such that p^2+4 is a prime times 5^n](./oeis-research/J.%20M.%20Bergot/a(n)%20is%20the%20least%20prime%20p%20such%20that%20p^2+4%20is%20a%20prime%20times%205^n)
            * [modular equation solutions.sf](./oeis-research/J.%20M.%20Bergot/a(n)%20is%20the%20least%20prime%20p%20such%20that%20p^2+4%20is%20a%20prime%20times%205^n/modular_equation_solutions.sf)
            * [simplified prog.sf](./oeis-research/J.%20M.%20Bergot/a(n)%20is%20the%20least%20prime%20p%20such%20that%20p^2+4%20is%20a%20prime%20times%205^n/simplified_prog.sf)
        * [A(n) is the least prime p such that there exists a prime q with p^2 + n = (n+1)*q^2, or 0 if there is no such p](./oeis-research/J.%20M.%20Bergot/a(n)%20is%20the%20least%20prime%20p%20such%20that%20there%20exists%20a%20prime%20q%20with%20p^2%20+%20n%20=%20(n+1)*q^2,%20or%200%20if%20there%20is%20no%20such%20p)
            * [find a16.sf](./oeis-research/J.%20M.%20Bergot/a(n)%20is%20the%20least%20prime%20p%20such%20that%20there%20exists%20a%20prime%20q%20with%20p^2%20+%20n%20=%20(n+1)*q^2,%20or%200%20if%20there%20is%20no%20such%20p/find_a16.sf)
        * [A(n) is the least prime p that is the first of three consecutive primes p, q, r such that p^i + q^i - r^i is prime for i from 1 to n but not n+1](./oeis-research/J.%20M.%20Bergot/a(n)%20is%20the%20least%20prime%20p%20that%20is%20the%20first%20of%20three%20consecutive%20primes%20p,%20q,%20r%20such%20that%20p^i%20+%20q^i%20-%20r^i%20is%20prime%20for%20i%20from%201%20to%20n%20but%20not%20n+1)
            * [prog.pl](./oeis-research/J.%20M.%20Bergot/a(n)%20is%20the%20least%20prime%20p%20that%20is%20the%20first%20of%20three%20consecutive%20primes%20p,%20q,%20r%20such%20that%20p^i%20+%20q^i%20-%20r^i%20is%20prime%20for%20i%20from%201%20to%20n%20but%20not%20n+1/prog.pl)
        * [A(n) is the least prime prime(k) such that prime(k+n-1)^2 - prime(k)^2 + prime(i) for i=k..k+n-1 are consecutive primes](./oeis-research/J.%20M.%20Bergot/a(n)%20is%20the%20least%20prime%20prime(k)%20such%20that%20prime(k+n-1)^2%20-%20prime(k)^2%20+%20prime(i)%20for%20i=k..k+n-1%20are%20consecutive%20primes)
            * [prog.pl](./oeis-research/J.%20M.%20Bergot/a(n)%20is%20the%20least%20prime%20prime(k)%20such%20that%20prime(k+n-1)^2%20-%20prime(k)^2%20+%20prime(i)%20for%20i=k..k+n-1%20are%20consecutive%20primes/prog.pl)
        * [First emirp p that starts a sequence of n emirps x(1),...,x(n) with x(1) = p and x(k+1) = 2*x(k) - reverse(x(k)), but 2*x(n) - reverse(x(n)) is not an emirp](./oeis-research/J.%20M.%20Bergot/First%20emirp%20p%20that%20starts%20a%20sequence%20of%20n%20emirps%20x(1),...,x(n)%20with%20x(1)%20=%20p%20and%20x(k+1)%20=%202*x(k)%20-%20reverse(x(k)),%20but%202*x(n)%20-%20reverse(x(n))%20is%20not%20an%20emirp)
            * [prog.pl](./oeis-research/J.%20M.%20Bergot/First%20emirp%20p%20that%20starts%20a%20sequence%20of%20n%20emirps%20x(1),...,x(n)%20with%20x(1)%20=%20p%20and%20x(k+1)%20=%202*x(k)%20-%20reverse(x(k)),%20but%202*x(n)%20-%20reverse(x(n))%20is%20not%20an%20emirp/prog.pl)
            * [prog 2.pl](./oeis-research/J.%20M.%20Bergot/First%20emirp%20p%20that%20starts%20a%20sequence%20of%20n%20emirps%20x(1),...,x(n)%20with%20x(1)%20=%20p%20and%20x(k+1)%20=%202*x(k)%20-%20reverse(x(k)),%20but%202*x(n)%20-%20reverse(x(n))%20is%20not%20an%20emirp/prog_2.pl)
            * [prog 3.pl](./oeis-research/J.%20M.%20Bergot/First%20emirp%20p%20that%20starts%20a%20sequence%20of%20n%20emirps%20x(1),...,x(n)%20with%20x(1)%20=%20p%20and%20x(k+1)%20=%202*x(k)%20-%20reverse(x(k)),%20but%202*x(n)%20-%20reverse(x(n))%20is%20not%20an%20emirp/prog_3.pl)
        * [Numbers k such that A124440(k) is a square](./oeis-research/J.%20M.%20Bergot/Numbers%20k%20such%20that%20A124440(k)%20is%20a%20square)
            * [prog.gp](./oeis-research/J.%20M.%20Bergot/Numbers%20k%20such%20that%20A124440(k)%20is%20a%20square/prog.gp)
        * [Numbers k such that prime(k)^prime(k+1) == prime(k+3) (mod prime(k+2))](./oeis-research/J.%20M.%20Bergot/Numbers%20k%20such%20that%20prime(k)^prime(k+1)%20==%20prime(k+3)%20(mod%20prime(k+2)))
            * [prog.pl](./oeis-research/J.%20M.%20Bergot/Numbers%20k%20such%20that%20prime(k)^prime(k+1)%20==%20prime(k+3)%20(mod%20prime(k+2))/prog.pl)
            * [sieve cluster.pl](./oeis-research/J.%20M.%20Bergot/Numbers%20k%20such%20that%20prime(k)^prime(k+1)%20==%20prime(k+3)%20(mod%20prime(k+2))/sieve_cluster.pl)
        * [Numbers k such that the k-th triangular number mod sopfr(k), and the k-th triangular number mod sigma(k), are the same prime](./oeis-research/J.%20M.%20Bergot/Numbers%20k%20such%20that%20the%20k-th%20triangular%20number%20mod%20sopfr(k),%20and%20the%20k-th%20triangular%20number%20mod%20sigma(k),%20are%20the%20same%20prime)
            * [prog.pl](./oeis-research/J.%20M.%20Bergot/Numbers%20k%20such%20that%20the%20k-th%20triangular%20number%20mod%20sopfr(k),%20and%20the%20k-th%20triangular%20number%20mod%20sigma(k),%20are%20the%20same%20prime/prog.pl)
        * [Primes p such that (2^p+p^2) over 3 is prime](./oeis-research/J.%20M.%20Bergot/Primes%20p%20such%20that%20(2^p+p^2)%20over%203%20is%20prime)
            * [prog.sf](./oeis-research/J.%20M.%20Bergot/Primes%20p%20such%20that%20(2^p+p^2)%20over%203%20is%20prime/prog.sf)
        * [Primes p such that the sum of squares of primes < p is divisible by p](./oeis-research/J.%20M.%20Bergot/Primes%20p%20such%20that%20the%20sum%20of%20squares%20of%20primes%20<%20p%20is%20divisible%20by%20p)
            * [search.pl](./oeis-research/J.%20M.%20Bergot/Primes%20p%20such%20that%20the%20sum%20of%20squares%20of%20primes%20<%20p%20is%20divisible%20by%20p/search.pl)
        * [Primes p such that, with q the next prime after p, q > p+2 and q^p == q (mod p+q) and p^q == p (mod p+q)](./oeis-research/J.%20M.%20Bergot/Primes%20p%20such%20that,%20with%20q%20the%20next%20prime%20after%20p,%20q%20>%20p+2%20and%20q^p%20==%20q%20(mod%20p+q)%20and%20p^q%20==%20p%20(mod%20p+q))
            * [prog.pl](./oeis-research/J.%20M.%20Bergot/Primes%20p%20such%20that,%20with%20q%20the%20next%20prime%20after%20p,%20q%20>%20p+2%20and%20q^p%20==%20q%20(mod%20p+q)%20and%20p^q%20==%20p%20(mod%20p+q)/prog.pl)
        * [Semiprimes p*q with p <= q such that Sum {primes r <= p} (q mod r) = q](./oeis-research/J.%20M.%20Bergot/Semiprimes%20p*q%20with%20p%20<=%20q%20such%20that%20Sum_{primes%20r%20<=%20p}%20(q%20mod%20r)%20=%20q)
            * [search.pl](./oeis-research/J.%20M.%20Bergot/Semiprimes%20p*q%20with%20p%20<=%20q%20such%20that%20Sum_{primes%20r%20<=%20p}%20(q%20mod%20r)%20=%20q/search.pl)
        * [Smallest k having n prime factors such that k + sum of the prime factors of k also has n prime factors](./oeis-research/J.%20M.%20Bergot/Smallest%20k%20having%20n%20prime%20factors%20such%20that%20k%20+%20sum%20of%20the%20prime%20factors%20of%20k%20also%20has%20n%20prime%20factors)
            * [prog.pl](./oeis-research/J.%20M.%20Bergot/Smallest%20k%20having%20n%20prime%20factors%20such%20that%20k%20+%20sum%20of%20the%20prime%20factors%20of%20k%20also%20has%20n%20prime%20factors/prog.pl)
        * [Smallest k such that n = bigomega(k) = bigomega(k-1) + bigomega(k+1)](./oeis-research/J.%20M.%20Bergot/Smallest%20k%20such%20that%20n%20=%20bigomega(k)%20=%20bigomega(k-1)%20+%20bigomega(k+1))
            * [generate.pl](./oeis-research/J.%20M.%20Bergot/Smallest%20k%20such%20that%20n%20=%20bigomega(k)%20=%20bigomega(k-1)%20+%20bigomega(k+1)/generate.pl)
            * [generate.sf](./oeis-research/J.%20M.%20Bergot/Smallest%20k%20such%20that%20n%20=%20bigomega(k)%20=%20bigomega(k-1)%20+%20bigomega(k+1)/generate.sf)
            * [search.pl](./oeis-research/J.%20M.%20Bergot/Smallest%20k%20such%20that%20n%20=%20bigomega(k)%20=%20bigomega(k-1)%20+%20bigomega(k+1)/search.pl)
            * [upper-bounds.pl](./oeis-research/J.%20M.%20Bergot/Smallest%20k%20such%20that%20n%20=%20bigomega(k)%20=%20bigomega(k-1)%20+%20bigomega(k+1)/upper-bounds.pl)
        * [Smallest prime p such that p-1 and p+1 both have n prime factors (with multiplicity)](./oeis-research/J.%20M.%20Bergot/Smallest%20prime%20p%20such%20that%20p-1%20and%20p+1%20both%20have%20n%20prime%20factors%20(with%20multiplicity))
            * [generate.pl](./oeis-research/J.%20M.%20Bergot/Smallest%20prime%20p%20such%20that%20p-1%20and%20p+1%20both%20have%20n%20prime%20factors%20(with%20multiplicity)/generate.pl)
            * [prog ntheory.pl](./oeis-research/J.%20M.%20Bergot/Smallest%20prime%20p%20such%20that%20p-1%20and%20p+1%20both%20have%20n%20prime%20factors%20(with%20multiplicity)/prog_ntheory.pl)
    * [J.W.L. (Jan) Eerland](./oeis-research/J.W.L.%20(Jan)%20Eerland)
        * [Least prime p such that p + 4*k*(k+1) is prime for 0 <= k <= n-1 but not for k=n](./oeis-research/J.W.L.%20(Jan)%20Eerland/Least%20prime%20p%20such%20that%20p%20+%204*k*(k+1)%20is%20prime%20for%200%20<=%20k%20<=%20n-1%20but%20not%20for%20k=n)
            * [sieve.pl](./oeis-research/J.W.L.%20(Jan)%20Eerland/Least%20prime%20p%20such%20that%20p%20+%204*k*(k+1)%20is%20prime%20for%200%20<=%20k%20<=%20n-1%20but%20not%20for%20k=n/sieve.pl)
        * [Least prime p such that p + 6*k*(k+1) is prime for 0 <= k <= n-1 but not for k=n](./oeis-research/J.W.L.%20(Jan)%20Eerland/Least%20prime%20p%20such%20that%20p%20+%206*k*(k+1)%20is%20prime%20for%200%20<=%20k%20<=%20n-1%20but%20not%20for%20k=n)
            * [sieve.pl](./oeis-research/J.W.L.%20(Jan)%20Eerland/Least%20prime%20p%20such%20that%20p%20+%206*k*(k+1)%20is%20prime%20for%200%20<=%20k%20<=%20n-1%20but%20not%20for%20k=n/sieve.pl)
        * [Least prime p such that p + 7*k*(k+1) is prime for 0 <= k <= n-1 but not for k=n](./oeis-research/J.W.L.%20(Jan)%20Eerland/Least%20prime%20p%20such%20that%20p%20+%207*k*(k+1)%20is%20prime%20for%200%20<=%20k%20<=%20n-1%20but%20not%20for%20k=n)
            * [sieve.pl](./oeis-research/J.W.L.%20(Jan)%20Eerland/Least%20prime%20p%20such%20that%20p%20+%207*k*(k+1)%20is%20prime%20for%200%20<=%20k%20<=%20n-1%20but%20not%20for%20k=n/sieve.pl)
        * [Least prime p such that p + 8*k*(k+1) is prime for 0 <= k <= n-1 but not for k=n](./oeis-research/J.W.L.%20(Jan)%20Eerland/Least%20prime%20p%20such%20that%20p%20+%208*k*(k+1)%20is%20prime%20for%200%20<=%20k%20<=%20n-1%20but%20not%20for%20k=n)
            * [sieve.pl](./oeis-research/J.W.L.%20(Jan)%20Eerland/Least%20prime%20p%20such%20that%20p%20+%208*k*(k+1)%20is%20prime%20for%200%20<=%20k%20<=%20n-1%20but%20not%20for%20k=n/sieve.pl)
        * [Least prime p such that p + 9*k*(k+1) is prime for 0 <= k <= n-1 but not for k=n](./oeis-research/J.W.L.%20(Jan)%20Eerland/Least%20prime%20p%20such%20that%20p%20+%209*k*(k+1)%20is%20prime%20for%200%20<=%20k%20<=%20n-1%20but%20not%20for%20k=n)
            * [sieve.pl](./oeis-research/J.W.L.%20(Jan)%20Eerland/Least%20prime%20p%20such%20that%20p%20+%209*k*(k+1)%20is%20prime%20for%200%20<=%20k%20<=%20n-1%20but%20not%20for%20k=n/sieve.pl)
        * [Least prime p such that p^n + 2 is the product of n distinct primes](./oeis-research/J.W.L.%20(Jan)%20Eerland/Least%20prime%20p%20such%20that%20p^n%20+%202%20is%20the%20product%20of%20n%20distinct%20primes)
            * [is squarefree omega prime.sf](./oeis-research/J.W.L.%20(Jan)%20Eerland/Least%20prime%20p%20such%20that%20p^n%20+%202%20is%20the%20product%20of%20n%20distinct%20primes/is_squarefree_omega_prime.sf)
            * [prog.sf](./oeis-research/J.W.L.%20(Jan)%20Eerland/Least%20prime%20p%20such%20that%20p^n%20+%202%20is%20the%20product%20of%20n%20distinct%20primes/prog.sf)
        * [Least prime p such that p^n + 4 is the product of n distinct primes](./oeis-research/J.W.L.%20(Jan)%20Eerland/Least%20prime%20p%20such%20that%20p^n%20+%204%20is%20the%20product%20of%20n%20distinct%20primes)
            * [is squarefree omega prime.sf](./oeis-research/J.W.L.%20(Jan)%20Eerland/Least%20prime%20p%20such%20that%20p^n%20+%204%20is%20the%20product%20of%20n%20distinct%20primes/is_squarefree_omega_prime.sf)
        * [Least prime p such that p^n + 6 is the product of n distinct primes](./oeis-research/J.W.L.%20(Jan)%20Eerland/Least%20prime%20p%20such%20that%20p^n%20+%206%20is%20the%20product%20of%20n%20distinct%20primes)
            * [is squarefree almost prime.sf](./oeis-research/J.W.L.%20(Jan)%20Eerland/Least%20prime%20p%20such%20that%20p^n%20+%206%20is%20the%20product%20of%20n%20distinct%20primes/is_squarefree_almost_prime.sf)
        * [Smallest k such that 3^(4*3^n) - k is a safe prime](./oeis-research/J.W.L.%20(Jan)%20Eerland/Smallest%20k%20such%20that%203^(4*3^n)%20-%20k%20is%20a%20safe%20prime)
            * [prog.sf](./oeis-research/J.W.L.%20(Jan)%20Eerland/Smallest%20k%20such%20that%203^(4*3^n)%20-%20k%20is%20a%20safe%20prime/prog.sf)
    * [Jacques Tramu](./oeis-research/Jacques%20Tramu)
        * [First odd prime in the (n-th)-order Fibonacci sequence Fn](./oeis-research/Jacques%20Tramu/First%20odd%20prime%20in%20the%20(n-th)-order%20Fibonacci%20sequence%20Fn)
            * [prog.pl](./oeis-research/Jacques%20Tramu/First%20odd%20prime%20in%20the%20(n-th)-order%20Fibonacci%20sequence%20Fn/prog.pl)
            * [prog pfgw.pl](./oeis-research/Jacques%20Tramu/First%20odd%20prime%20in%20the%20(n-th)-order%20Fibonacci%20sequence%20Fn/prog_pfgw.pl)
    * [James S. DeArmon](./oeis-research/James%20S.%20DeArmon)
        * [A(n) is the number of prime quadruples of the form {p, p+2, p+6, p+12} with p < 10^n](./oeis-research/James%20S.%20DeArmon/a(n)%20is%20the%20number%20of%20prime%20quadruples%20of%20the%20form%20{p,%20p+2,%20p+6,%20p+12}%20with%20p%20<%2010^n)
            * [prog.pl](./oeis-research/James%20S.%20DeArmon/a(n)%20is%20the%20number%20of%20prime%20quadruples%20of%20the%20form%20{p,%20p+2,%20p+6,%20p+12}%20with%20p%20<%2010^n/prog.pl)
    * [Jaroslav Krizek](./oeis-research/Jaroslav%20Krizek)
        * [Numbers n such that lcm(sigma(n), n) = tau(n) * sigma(n)](./oeis-research/Jaroslav%20Krizek/Numbers%20n%20such%20that%20lcm(sigma(n),%20n)%20=%20tau(n)%20*%20sigma(n))
            * [x.pl](./oeis-research/Jaroslav%20Krizek/Numbers%20n%20such%20that%20lcm(sigma(n),%20n)%20=%20tau(n)%20*%20sigma(n)/x.pl)
        * [Palindromes whose number and sum of divisors are both also palindromic](./oeis-research/Jaroslav%20Krizek/Palindromes%20whose%20number%20and%20sum%20of%20divisors%20are%20both%20also%20palindromic)
            * [prog.pl](./oeis-research/Jaroslav%20Krizek/Palindromes%20whose%20number%20and%20sum%20of%20divisors%20are%20both%20also%20palindromic/prog.pl)
        * [Sum of primes divisible by n](./oeis-research/Jaroslav%20Krizek/Sum%20of%20primes%20divisible%20by%20n)
            * [new.pl](./oeis-research/Jaroslav%20Krizek/Sum%20of%20primes%20divisible%20by%20n/new.pl)
            * [new v2.pl](./oeis-research/Jaroslav%20Krizek/Sum%20of%20primes%20divisible%20by%20n/new_v2.pl)
    * [Jason Earls](./oeis-research/Jason%20Earls)
        * [A(1) = 1, a(n) = largest prime divisor of A057137](./oeis-research/Jason%20Earls/a(1)%20=%201,%20a(n)%20=%20largest%20prime%20divisor%20of%20A057137)
            * [prog.sf](./oeis-research/Jason%20Earls/a(1)%20=%201,%20a(n)%20=%20largest%20prime%20divisor%20of%20A057137/prog.sf)
        * [Largest prime factor of 9^(2n)+1 (A063270)](./oeis-research/Jason%20Earls/Largest%20prime%20factor%20of%209^(2n)+1%20(A063270))
            * [prog.sf](./oeis-research/Jason%20Earls/Largest%20prime%20factor%20of%209^(2n)+1%20(A063270)/prog.sf)
        * [Largest prime factor of A019518, concatenation of first n primes](./oeis-research/Jason%20Earls/Largest%20prime%20factor%20of%20A019518,%20concatenation%20of%20first%20n%20primes)
            * [prog.sf](./oeis-research/Jason%20Earls/Largest%20prime%20factor%20of%20A019518,%20concatenation%20of%20first%20n%20primes/prog.sf)
        * [Largest prime factor of the integer formed by truncating the decimal expansion of Pi to n places](./oeis-research/Jason%20Earls/Largest%20prime%20factor%20of%20the%20integer%20formed%20by%20truncating%20the%20decimal%20expansion%20of%20Pi%20to%20n%20places)
            * [prog.sf](./oeis-research/Jason%20Earls/Largest%20prime%20factor%20of%20the%20integer%20formed%20by%20truncating%20the%20decimal%20expansion%20of%20Pi%20to%20n%20places/prog.sf)
        * [Number of brilliant numbers < 10^n](./oeis-research/Jason%20Earls/Number%20of%20brilliant%20numbers%20<%2010^n)
            * [prog.pl](./oeis-research/Jason%20Earls/Number%20of%20brilliant%20numbers%20<%2010^n/prog.pl)
        * [Number of factors of distinct prime factors of sum of p n primorials](./oeis-research/Jason%20Earls/Number%20of%20factors%20of%20distinct%20prime%20factors%20of%20sum%20of%20p_n%20primorials)
            * [prog.sf](./oeis-research/Jason%20Earls/Number%20of%20factors%20of%20distinct%20prime%20factors%20of%20sum%20of%20p_n%20primorials/prog.sf)
        * [Numbers that set a new record for number of Fibonacci divisors](./oeis-research/Jason%20Earls/Numbers%20that%20set%20a%20new%20record%20for%20number%20of%20Fibonacci%20divisors)
            * [smooth generate.pl](./oeis-research/Jason%20Earls/Numbers%20that%20set%20a%20new%20record%20for%20number%20of%20Fibonacci%20divisors/smooth_generate.pl)
        * [Prime pi equals sum of primes lpf and gpf](./oeis-research/Jason%20Earls/Prime%20pi%20equals%20sum%20of%20primes%20lpf%20and%20gpf)
            * [prog.pl](./oeis-research/Jason%20Earls/Prime%20pi%20equals%20sum%20of%20primes%20lpf%20and%20gpf/prog.pl)
    * [Jean-Marc Rebert](./oeis-research/Jean-Marc%20Rebert)
        * [Least number m such that 9*k*m+1 is prime for k=1..n](./oeis-research/Jean-Marc%20Rebert/Least%20number%20m%20such%20that%209*k*m+1%20is%20prime%20for%20k=1..n)
            * [prog.sf](./oeis-research/Jean-Marc%20Rebert/Least%20number%20m%20such%20that%209*k*m+1%20is%20prime%20for%20k=1..n/prog.sf)
        * [Least starting prime of exactly n consecutive primes p i (i = 1..n) such that bigomega(p i + 1) = 1 + i](./oeis-research/Jean-Marc%20Rebert/Least%20starting%20prime%20of%20exactly%20n%20consecutive%20primes%20p_i%20(i%20=%201..n)%20such%20that%20bigomega(p_i%20+%201)%20=%201%20+%20i)
            * [prog generate.pl](./oeis-research/Jean-Marc%20Rebert/Least%20starting%20prime%20of%20exactly%20n%20consecutive%20primes%20p_i%20(i%20=%201..n)%20such%20that%20bigomega(p_i%20+%201)%20=%201%20+%20i/prog_generate.pl)
            * [prog lazy iter.pl](./oeis-research/Jean-Marc%20Rebert/Least%20starting%20prime%20of%20exactly%20n%20consecutive%20primes%20p_i%20(i%20=%201..n)%20such%20that%20bigomega(p_i%20+%201)%20=%201%20+%20i/prog_lazy_iter.pl)
            * [prog lazy iter 2.pl](./oeis-research/Jean-Marc%20Rebert/Least%20starting%20prime%20of%20exactly%20n%20consecutive%20primes%20p_i%20(i%20=%201..n)%20such%20that%20bigomega(p_i%20+%201)%20=%201%20+%20i/prog_lazy_iter_2.pl)
        * [Least starting prime of exactly n consecutive primes p i (i = 1..n) such that omega(p i + 1) = 1 + i](./oeis-research/Jean-Marc%20Rebert/Least%20starting%20prime%20of%20exactly%20n%20consecutive%20primes%20p_i%20(i%20=%201..n)%20such%20that%20omega(p_i%20+%201)%20=%201%20+%20i)
            * [prog.sf](./oeis-research/Jean-Marc%20Rebert/Least%20starting%20prime%20of%20exactly%20n%20consecutive%20primes%20p_i%20(i%20=%201..n)%20such%20that%20omega(p_i%20+%201)%20=%201%20+%20i/prog.sf)
            * [prog generate.pl](./oeis-research/Jean-Marc%20Rebert/Least%20starting%20prime%20of%20exactly%20n%20consecutive%20primes%20p_i%20(i%20=%201..n)%20such%20that%20omega(p_i%20+%201)%20=%201%20+%20i/prog_generate.pl)
            * [prog lazy iter.pl](./oeis-research/Jean-Marc%20Rebert/Least%20starting%20prime%20of%20exactly%20n%20consecutive%20primes%20p_i%20(i%20=%201..n)%20such%20that%20omega(p_i%20+%201)%20=%201%20+%20i/prog_lazy_iter.pl)
        * [Numbers k such that the prime gap between the consecutive primes p1 < k! = factorial(k) < p2 sets a new record](./oeis-research/Jean-Marc%20Rebert/Numbers%20k%20such%20that%20the%20prime%20gap%20between%20the%20consecutive%20primes%20p1%20<%20k!%20=%20factorial(k)%20<%20p2%20sets%20a%20new%20record)
            * [prog.sf](./oeis-research/Jean-Marc%20Rebert/Numbers%20k%20such%20that%20the%20prime%20gap%20between%20the%20consecutive%20primes%20p1%20<%20k!%20=%20factorial(k)%20<%20p2%20sets%20a%20new%20record/prog.sf)
        * [Smallest number k such that both k^n - 1 and k^n + 1 have n prime factors, counted with repetitions](./oeis-research/Jean-Marc%20Rebert/Smallest%20number%20k%20such%20that%20both%20k^n%20-%201%20and%20k^n%20+%201%20have%20n%20prime%20factors,%20counted%20with%20repetitions)
            * [prog.sf](./oeis-research/Jean-Marc%20Rebert/Smallest%20number%20k%20such%20that%20both%20k^n%20-%201%20and%20k^n%20+%201%20have%20n%20prime%20factors,%20counted%20with%20repetitions/prog.sf)
        * [Smallest number k such that k-n and k+n are consecutive primes and k has exactly n distinct prime factors](./oeis-research/Jean-Marc%20Rebert/Smallest%20number%20k%20such%20that%20k-n%20and%20k+n%20are%20consecutive%20primes%20and%20k%20has%20exactly%20n%20distinct%20prime%20factors)
            * [prog mpz.pl](./oeis-research/Jean-Marc%20Rebert/Smallest%20number%20k%20such%20that%20k-n%20and%20k+n%20are%20consecutive%20primes%20and%20k%20has%20exactly%20n%20distinct%20prime%20factors/prog_mpz.pl)
            * [prog native.pl](./oeis-research/Jean-Marc%20Rebert/Smallest%20number%20k%20such%20that%20k-n%20and%20k+n%20are%20consecutive%20primes%20and%20k%20has%20exactly%20n%20distinct%20prime%20factors/prog_native.pl)
        * [Smallest prime p such that omega(q^2 - p^2) = n where q is the next prime after p](./oeis-research/Jean-Marc%20Rebert/Smallest%20prime%20p%20such%20that%20omega(q^2%20-%20p^2)%20=%20n%20where%20q%20is%20the%20next%20prime%20after%20p)
            * [generate.gp](./oeis-research/Jean-Marc%20Rebert/Smallest%20prime%20p%20such%20that%20omega(q^2%20-%20p^2)%20=%20n%20where%20q%20is%20the%20next%20prime%20after%20p/generate.gp)
            * [generate.sf](./oeis-research/Jean-Marc%20Rebert/Smallest%20prime%20p%20such%20that%20omega(q^2%20-%20p^2)%20=%20n%20where%20q%20is%20the%20next%20prime%20after%20p/generate.sf)
            * [generate 2.gp](./oeis-research/Jean-Marc%20Rebert/Smallest%20prime%20p%20such%20that%20omega(q^2%20-%20p^2)%20=%20n%20where%20q%20is%20the%20next%20prime%20after%20p/generate_2.gp)
            * [generate 2.sf](./oeis-research/Jean-Marc%20Rebert/Smallest%20prime%20p%20such%20that%20omega(q^2%20-%20p^2)%20=%20n%20where%20q%20is%20the%20next%20prime%20after%20p/generate_2.sf)
    * [Jeff Burch](./oeis-research/Jeff%20Burch)
        * [Least k such that the period of continued fraction for sqrt(k) has at least n successive 1s](./oeis-research/Jeff%20Burch/Least%20k%20such%20that%20the%20period%20of%20continued%20fraction%20for%20sqrt(k)%20has%20at%20least%20n%20successive%201s)
            * [prog.cpp](./oeis-research/Jeff%20Burch/Least%20k%20such%20that%20the%20period%20of%20continued%20fraction%20for%20sqrt(k)%20has%20at%20least%20n%20successive%201s/prog.cpp)
    * [Jeppe Stig Nielsen](./oeis-research/Jeppe%20Stig%20Nielsen)
        * [Smallest base-2 even pseudoprime (A006935) with exactly n prime factors, or 0 if no such number exists](./oeis-research/Jeppe%20Stig%20Nielsen/Smallest%20base-2%20even%20pseudoprime%20(A006935)%20with%20exactly%20n%20prime%20factors,%20or%200%20if%20no%20such%20number%20exists)
            * [prog.jl](./oeis-research/Jeppe%20Stig%20Nielsen/Smallest%20base-2%20even%20pseudoprime%20(A006935)%20with%20exactly%20n%20prime%20factors,%20or%200%20if%20no%20such%20number%20exists/prog.jl)
            * [prog.pl](./oeis-research/Jeppe%20Stig%20Nielsen/Smallest%20base-2%20even%20pseudoprime%20(A006935)%20with%20exactly%20n%20prime%20factors,%20or%200%20if%20no%20such%20number%20exists/prog.pl)
            * [prog.sf](./oeis-research/Jeppe%20Stig%20Nielsen/Smallest%20base-2%20even%20pseudoprime%20(A006935)%20with%20exactly%20n%20prime%20factors,%20or%200%20if%20no%20such%20number%20exists/prog.sf)
            * [upper-bounds.pl](./oeis-research/Jeppe%20Stig%20Nielsen/Smallest%20base-2%20even%20pseudoprime%20(A006935)%20with%20exactly%20n%20prime%20factors,%20or%200%20if%20no%20such%20number%20exists/upper-bounds.pl)
    * [Jianing Song](./oeis-research/Jianing%20Song)
        * [Composite numbers k such that the multiplicative order of 2 modulo lpf(2^k-1) is k](./oeis-research/Jianing%20Song/Composite%20numbers%20k%20such%20that%20the%20multiplicative%20order%20of%202%20modulo%20lpf(2^k-1)%20is%20k)
            * [prog.sf](./oeis-research/Jianing%20Song/Composite%20numbers%20k%20such%20that%20the%20multiplicative%20order%20of%202%20modulo%20lpf(2^k-1)%20is%20k/prog.sf)
        * [Least Carmichael number (A002997) that is the product of exactly n primes congruent to 3 modulo 4](./oeis-research/Jianing%20Song/Least%20Carmichael%20number%20(A002997)%20that%20is%20the%20product%20of%20exactly%20n%20primes%20congruent%20to%203%20modulo%204)
            * [generate.pl](./oeis-research/Jianing%20Song/Least%20Carmichael%20number%20(A002997)%20that%20is%20the%20product%20of%20exactly%20n%20primes%20congruent%20to%203%20modulo%204/generate.pl)
        * [Least coprime quadratic nonresidue to a(n)](./oeis-research/Jianing%20Song/Least%20coprime%20quadratic%20nonresidue%20to%20a(n))
            * [ntheory-sqrtmod.pl](./oeis-research/Jianing%20Song/Least%20coprime%20quadratic%20nonresidue%20to%20a(n)/ntheory-sqrtmod.pl)
            * [sidef-sqrtmod.pl](./oeis-research/Jianing%20Song/Least%20coprime%20quadratic%20nonresidue%20to%20a(n)/sidef-sqrtmod.pl)
            * [tmp.pl](./oeis-research/Jianing%20Song/Least%20coprime%20quadratic%20nonresidue%20to%20a(n)/tmp.pl)
    * [Jinyuan Wang](./oeis-research/Jinyuan%20Wang)
        * [Least totient number k > 1 such that n*k is a nontotient number, or 0 if no such number exists](./oeis-research/Jinyuan%20Wang/Least%20totient%20number%20k%20>%201%20such%20that%20n*k%20is%20a%20nontotient%20number,%20or%200%20if%20no%20such%20number%20exists)
            * [prog.sf](./oeis-research/Jinyuan%20Wang/Least%20totient%20number%20k%20>%201%20such%20that%20n*k%20is%20a%20nontotient%20number,%20or%200%20if%20no%20such%20number%20exists/prog.sf)
        * [Numbers k such that 4^k - 3^k + 2^k is prime](./oeis-research/Jinyuan%20Wang/Numbers%20k%20such%20that%204^k%20-%203^k%20+%202^k%20is%20prime)
            * [prog.sf](./oeis-research/Jinyuan%20Wang/Numbers%20k%20such%20that%204^k%20-%203^k%20+%202^k%20is%20prime/prog.sf)
        * [Run of n primes when 3*x - 2 is iterated](./oeis-research/Jinyuan%20Wang/Run%20of%20n%20primes%20when%203*x%20-%202%20is%20iterated)
            * [prog.pl](./oeis-research/Jinyuan%20Wang/Run%20of%20n%20primes%20when%203*x%20-%202%20is%20iterated/prog.pl)
        * [Smallest Euler-Jacobi pseudoprime to all natural bases up to prime(n) - 1 that is not a base prime(n) Euler-Jacobi pseudoprime](./oeis-research/Jinyuan%20Wang/Smallest%20Euler-Jacobi%20pseudoprime%20to%20all%20natural%20bases%20up%20to%20prime(n)%20-%201%20that%20is%20not%20a%20base%20prime(n)%20Euler-Jacobi%20pseudoprime)
            * [prog.pl](./oeis-research/Jinyuan%20Wang/Smallest%20Euler-Jacobi%20pseudoprime%20to%20all%20natural%20bases%20up%20to%20prime(n)%20-%201%20that%20is%20not%20a%20base%20prime(n)%20Euler-Jacobi%20pseudoprime/prog.pl)
            * [prog alt.pl](./oeis-research/Jinyuan%20Wang/Smallest%20Euler-Jacobi%20pseudoprime%20to%20all%20natural%20bases%20up%20to%20prime(n)%20-%201%20that%20is%20not%20a%20base%20prime(n)%20Euler-Jacobi%20pseudoprime/prog_alt.pl)
    * [Jon E. Schoenfield](./oeis-research/Jon%20E.%20Schoenfield)
        * [Largest prime factor of the n-th Pell number](./oeis-research/Jon%20E.%20Schoenfield/Largest%20prime%20factor%20of%20the%20n-th%20Pell%20number)
            * [prog.sf](./oeis-research/Jon%20E.%20Schoenfield/Largest%20prime%20factor%20of%20the%20n-th%20Pell%20number/prog.sf)
        * [Smallest prime p such that p + 6*t is also prime for every triangular number](./oeis-research/Jon%20E.%20Schoenfield/Smallest%20prime%20p%20such%20that%20p%20+%206*t%20is%20also%20prime%20for%20every%20triangular%20number)
            * [prog.pl](./oeis-research/Jon%20E.%20Schoenfield/Smallest%20prime%20p%20such%20that%20p%20+%206*t%20is%20also%20prime%20for%20every%20triangular%20number/prog.pl)
    * [Jonathan Sondow](./oeis-research/Jonathan%20Sondow)
        * [Largest prime factor of numerator of Sum {k=0..n} factorial(k)^(-1)](./oeis-research/Jonathan%20Sondow/Largest%20prime%20factor%20of%20numerator%20of%20Sum_{k=0..n}%20factorial(k)^(-1))
            * [prog.sf](./oeis-research/Jonathan%20Sondow/Largest%20prime%20factor%20of%20numerator%20of%20Sum_{k=0..n}%20factorial(k)^(-1)/prog.sf)
    * [Jonathan Vos Post](./oeis-research/Jonathan%20Vos%20Post)
        * [A(n) = k is the smallest number such that k^3 + 1 has exactly n distinct prime factors](./oeis-research/Jonathan%20Vos%20Post/a(n)%20=%20k%20is%20the%20smallest%20number%20such%20that%20k^3%20+%201%20has%20exactly%20n%20distinct%20prime%20factors)
            * [generate.pl](./oeis-research/Jonathan%20Vos%20Post/a(n)%20=%20k%20is%20the%20smallest%20number%20such%20that%20k^3%20+%201%20has%20exactly%20n%20distinct%20prime%20factors/generate.pl)
            * [upper-bounds.pl](./oeis-research/Jonathan%20Vos%20Post/a(n)%20=%20k%20is%20the%20smallest%20number%20such%20that%20k^3%20+%201%20has%20exactly%20n%20distinct%20prime%20factors/upper-bounds.pl)
    * [Joseph Biberstine](./oeis-research/Joseph%20Biberstine)
        * [Sum of remainders of the n-th prime mod k, for k = 1..n](./oeis-research/Joseph%20Biberstine/Sum%20of%20remainders%20of%20the%20n-th%20prime%20mod%20k,%20for%20k%20=%201..n)
            * [prog.sf](./oeis-research/Joseph%20Biberstine/Sum%20of%20remainders%20of%20the%20n-th%20prime%20mod%20k,%20for%20k%20=%201..n/prog.sf)
    * [José María Grau Ribas](./oeis-research/José%20María%20Grau%20Ribas)
        * [Numbers n such that phi(n) divides n+1, where phi is Euler's totient function (A000010)](./oeis-research/José%20María%20Grau%20Ribas/Numbers%20n%20such%20that%20phi(n)%20divides%20n+1,%20where%20phi%20is%20Euler's%20totient%20function%20(A000010))
            * [erdos generation method.pl](./oeis-research/José%20María%20Grau%20Ribas/Numbers%20n%20such%20that%20phi(n)%20divides%20n+1,%20where%20phi%20is%20Euler's%20totient%20function%20(A000010)/erdos_generation_method.pl)
            * [from smooth multiple.sf](./oeis-research/José%20María%20Grau%20Ribas/Numbers%20n%20such%20that%20phi(n)%20divides%20n+1,%20where%20phi%20is%20Euler's%20totient%20function%20(A000010)/from_smooth_multiple.sf)
            * [inverse phi.pl](./oeis-research/José%20María%20Grau%20Ribas/Numbers%20n%20such%20that%20phi(n)%20divides%20n+1,%20where%20phi%20is%20Euler's%20totient%20function%20(A000010)/inverse_phi.pl)
            * [smooth generate.pl](./oeis-research/José%20María%20Grau%20Ribas/Numbers%20n%20such%20that%20phi(n)%20divides%20n+1,%20where%20phi%20is%20Euler's%20totient%20function%20(A000010)/smooth_generate.pl)
    * [Jud McCranie](./oeis-research/Jud%20McCranie)
        * [Even numbers k such that k^2 - 1 is a powerful number](./oeis-research/Jud%20McCranie/Even%20numbers%20k%20such%20that%20k^2%20-%201%20is%20a%20powerful%20number)
            * [prog.pl](./oeis-research/Jud%20McCranie/Even%20numbers%20k%20such%20that%20k^2%20-%201%20is%20a%20powerful%20number/prog.pl)
            * [prog.sf](./oeis-research/Jud%20McCranie/Even%20numbers%20k%20such%20that%20k^2%20-%201%20is%20a%20powerful%20number/prog.sf)
        * [Solutions to sigma(n)+7 = sigma(n+7)](./oeis-research/Jud%20McCranie/Solutions%20to%20sigma(n)+7%20=%20sigma(n+7))
            * [special form.sf](./oeis-research/Jud%20McCranie/Solutions%20to%20sigma(n)+7%20=%20sigma(n+7)/special_form.sf)
    * [Julien Peter Benney](./oeis-research/Julien%20Peter%20Benney)
        * [Indices of prime Pell numbers](./oeis-research/Julien%20Peter%20Benney/Indices%20of%20prime%20Pell%20numbers)
            * [prog.pl](./oeis-research/Julien%20Peter%20Benney/Indices%20of%20prime%20Pell%20numbers/prog.pl)
    * [Juri-Stepan Gerasimov](./oeis-research/Juri-Stepan%20Gerasimov)
        * [A(n) is the least k>1 such that omega(k) is equal to (omega(n*k + 1) - 1) over n](./oeis-research/Juri-Stepan%20Gerasimov/a(n)%20is%20the%20least%20k>1%20such%20that%20omega(k)%20is%20equal%20to%20(omega(n*k%20+%201)%20-%201)%20over%20n)
            * [upper-bounds.sf](./oeis-research/Juri-Stepan%20Gerasimov/a(n)%20is%20the%20least%20k>1%20such%20that%20omega(k)%20is%20equal%20to%20(omega(n*k%20+%201)%20-%201)%20over%20n/upper-bounds.sf)
        * [A(n) is the smallest number in [2^(n-1) + 1..3^(n-1)] with exactly n divisors](./oeis-research/Juri-Stepan%20Gerasimov/a(n)%20is%20the%20smallest%20number%20in%20[2^(n-1)%20+%201..3^(n-1)]%20with%20exactly%20n%20divisors)
            * [prog.sf](./oeis-research/Juri-Stepan%20Gerasimov/a(n)%20is%20the%20smallest%20number%20in%20[2^(n-1)%20+%201..3^(n-1)]%20with%20exactly%20n%20divisors/prog.sf)
        * [Integers k such that the k-th prime divides the k-th Lucas number](./oeis-research/Juri-Stepan%20Gerasimov/Integers%20k%20such%20that%20the%20k-th%20prime%20divides%20the%20k-th%20Lucas%20number)
            * [search.pl](./oeis-research/Juri-Stepan%20Gerasimov/Integers%20k%20such%20that%20the%20k-th%20prime%20divides%20the%20k-th%20Lucas%20number/search.pl)
        * [Largest integer k < 2^(n-1) for which the number of divisors is equal to n](./oeis-research/Juri-Stepan%20Gerasimov/Largest%20integer%20k%20<%202^(n-1)%20for%20which%20the%20number%20of%20divisors%20is%20equal%20to%20n)
            * [generate.pl](./oeis-research/Juri-Stepan%20Gerasimov/Largest%20integer%20k%20<%202^(n-1)%20for%20which%20the%20number%20of%20divisors%20is%20equal%20to%20n/generate.pl)
            * [generate.sf](./oeis-research/Juri-Stepan%20Gerasimov/Largest%20integer%20k%20<%202^(n-1)%20for%20which%20the%20number%20of%20divisors%20is%20equal%20to%20n/generate.sf)
            * [prog.sf](./oeis-research/Juri-Stepan%20Gerasimov/Largest%20integer%20k%20<%202^(n-1)%20for%20which%20the%20number%20of%20divisors%20is%20equal%20to%20n/prog.sf)
        * [Largest prime factor of n^n - n^(n-1) - n^(n-2) - ... - n^2 - n - 1](./oeis-research/Juri-Stepan%20Gerasimov/Largest%20prime%20factor%20of%20n^n%20-%20n^(n-1)%20-%20n^(n-2)%20-%20...%20-%20n^2%20-%20n%20-%201)
            * [prog.sf](./oeis-research/Juri-Stepan%20Gerasimov/Largest%20prime%20factor%20of%20n^n%20-%20n^(n-1)%20-%20n^(n-2)%20-%20...%20-%20n^2%20-%20n%20-%201/prog.sf)
        * [Number of integers k in [prime(n-1)^7..prime(n)^7-1] with exactly 8 divisors](./oeis-research/Juri-Stepan%20Gerasimov/Number%20of%20integers%20k%20in%20[prime(n-1)^7..prime(n)^7-1]%20with%20exactly%208%20divisors)
            * [prog.sf](./oeis-research/Juri-Stepan%20Gerasimov/Number%20of%20integers%20k%20in%20[prime(n-1)^7..prime(n)^7-1]%20with%20exactly%208%20divisors/prog.sf)
            * [prog 2.sf](./oeis-research/Juri-Stepan%20Gerasimov/Number%20of%20integers%20k%20in%20[prime(n-1)^7..prime(n)^7-1]%20with%20exactly%208%20divisors/prog_2.sf)
        * [Number of k <= 2^(n-1) such that tau(k) = n](./oeis-research/Juri-Stepan%20Gerasimov/Number%20of%20k%20<=%202^(n-1)%20such%20that%20tau(k)%20=%20n)
            * [prog.gp](./oeis-research/Juri-Stepan%20Gerasimov/Number%20of%20k%20<=%202^(n-1)%20such%20that%20tau(k)%20=%20n/prog.gp)
            * [prog.pl](./oeis-research/Juri-Stepan%20Gerasimov/Number%20of%20k%20<=%202^(n-1)%20such%20that%20tau(k)%20=%20n/prog.pl)
            * [prog.sf](./oeis-research/Juri-Stepan%20Gerasimov/Number%20of%20k%20<=%202^(n-1)%20such%20that%20tau(k)%20=%20n/prog.sf)
            * [seq prog.pl](./oeis-research/Juri-Stepan%20Gerasimov/Number%20of%20k%20<=%202^(n-1)%20such%20that%20tau(k)%20=%20n/seq_prog.pl)
        * [Numbers k such that k^4*2^k - 1 is a prime](./oeis-research/Juri-Stepan%20Gerasimov/Numbers%20k%20such%20that%20k^4*2^k%20-%201%20is%20a%20prime)
            * [prog.sf](./oeis-research/Juri-Stepan%20Gerasimov/Numbers%20k%20such%20that%20k^4*2^k%20-%201%20is%20a%20prime/prog.sf)
        * [Numbers k such that omega(2^k-1) = omega(2*k-1)](./oeis-research/Juri-Stepan%20Gerasimov/Numbers%20k%20such%20that%20omega(2^k-1)%20=%20omega(2*k-1))
            * [prog.sf](./oeis-research/Juri-Stepan%20Gerasimov/Numbers%20k%20such%20that%20omega(2^k-1)%20=%20omega(2*k-1)/prog.sf)
        * [Numbers n such that n^(n + 1)*(n + 1)^n + 1 is prime](./oeis-research/Juri-Stepan%20Gerasimov/Numbers%20n%20such%20that%20n^(n%20+%201)*(n%20+%201)^n%20+%201%20is%20prime)
            * [search.sf](./oeis-research/Juri-Stepan%20Gerasimov/Numbers%20n%20such%20that%20n^(n%20+%201)*(n%20+%201)^n%20+%201%20is%20prime/search.sf)
        * [Numbers q such that (4*q^2-1)*2^q + 1 is prime](./oeis-research/Juri-Stepan%20Gerasimov/Numbers%20q%20such%20that%20(4*q^2-1)*2^q%20+%201%20is%20prime)
            * [prog.sf](./oeis-research/Juri-Stepan%20Gerasimov/Numbers%20q%20such%20that%20(4*q^2-1)*2^q%20+%201%20is%20prime/prog.sf)
        * [Primes p such that 2^p - p^2 is prime](./oeis-research/Juri-Stepan%20Gerasimov/Primes%20p%20such%20that%202^p%20-%20p^2%20is%20prime)
            * [prog.sf](./oeis-research/Juri-Stepan%20Gerasimov/Primes%20p%20such%20that%202^p%20-%20p^2%20is%20prime/prog.sf)
        * [Smallest k such that tau(k*2^n - 1) is equal to 2^n where tau = A000005](./oeis-research/Juri-Stepan%20Gerasimov/Smallest%20k%20such%20that%20tau(k*2^n%20-%201)%20is%20equal%20to%202^n%20where%20tau%20=%20A000005)
            * [generate.pl](./oeis-research/Juri-Stepan%20Gerasimov/Smallest%20k%20such%20that%20tau(k*2^n%20-%201)%20is%20equal%20to%202^n%20where%20tau%20=%20A000005/generate.pl)
            * [generate.sf](./oeis-research/Juri-Stepan%20Gerasimov/Smallest%20k%20such%20that%20tau(k*2^n%20-%201)%20is%20equal%20to%202^n%20where%20tau%20=%20A000005/generate.sf)
            * [generate bigomega primes.pl](./oeis-research/Juri-Stepan%20Gerasimov/Smallest%20k%20such%20that%20tau(k*2^n%20-%201)%20is%20equal%20to%202^n%20where%20tau%20=%20A000005/generate_bigomega_primes.pl)
            * [generate omega primes.pl](./oeis-research/Juri-Stepan%20Gerasimov/Smallest%20k%20such%20that%20tau(k*2^n%20-%201)%20is%20equal%20to%202^n%20where%20tau%20=%20A000005/generate_omega_primes.pl)
            * [prog.pl](./oeis-research/Juri-Stepan%20Gerasimov/Smallest%20k%20such%20that%20tau(k*2^n%20-%201)%20is%20equal%20to%202^n%20where%20tau%20=%20A000005/prog.pl)
            * [prog.sf](./oeis-research/Juri-Stepan%20Gerasimov/Smallest%20k%20such%20that%20tau(k*2^n%20-%201)%20is%20equal%20to%202^n%20where%20tau%20=%20A000005/prog.sf)
        * [Smallest positive number k such that k^2 - 1 and k^2 + 1 each have n distinct prime divisors](./oeis-research/Juri-Stepan%20Gerasimov/Smallest%20positive%20number%20k%20such%20that%20k^2%20-%201%20and%20k^2%20+%201%20each%20have%20n%20distinct%20prime%20divisors)
            * [generate fast.pl](./oeis-research/Juri-Stepan%20Gerasimov/Smallest%20positive%20number%20k%20such%20that%20k^2%20-%201%20and%20k^2%20+%201%20each%20have%20n%20distinct%20prime%20divisors/generate_fast.pl)
            * [prog.pl](./oeis-research/Juri-Stepan%20Gerasimov/Smallest%20positive%20number%20k%20such%20that%20k^2%20-%201%20and%20k^2%20+%201%20each%20have%20n%20distinct%20prime%20divisors/prog.pl)
            * [prog.sf](./oeis-research/Juri-Stepan%20Gerasimov/Smallest%20positive%20number%20k%20such%20that%20k^2%20-%201%20and%20k^2%20+%201%20each%20have%20n%20distinct%20prime%20divisors/prog.sf)
            * [upper bounds.pl](./oeis-research/Juri-Stepan%20Gerasimov/Smallest%20positive%20number%20k%20such%20that%20k^2%20-%201%20and%20k^2%20+%201%20each%20have%20n%20distinct%20prime%20divisors/upper_bounds.pl)
            * [upper bounds 2.pl](./oeis-research/Juri-Stepan%20Gerasimov/Smallest%20positive%20number%20k%20such%20that%20k^2%20-%201%20and%20k^2%20+%201%20each%20have%20n%20distinct%20prime%20divisors/upper_bounds_2.pl)
        * [Smallest prime p such that A005117(k+1) - A005117(k-1) = n, where p = A005117(k) for some k](./oeis-research/Juri-Stepan%20Gerasimov/Smallest%20prime%20p%20such%20that%20A005117(k+1)%20-%20A005117(k-1)%20=%20n,%20where%20p%20=%20A005117(k)%20for%20some%20k)
            * [prog.pl](./oeis-research/Juri-Stepan%20Gerasimov/Smallest%20prime%20p%20such%20that%20A005117(k+1)%20-%20A005117(k-1)%20=%20n,%20where%20p%20=%20A005117(k)%20for%20some%20k/prog.pl)
        * [Smallest prime p such that bigomega(p^n - 2) = bigomega(p^n + 2) = n](./oeis-research/Juri-Stepan%20Gerasimov/Smallest%20prime%20p%20such%20that%20bigomega(p^n%20-%202)%20=%20bigomega(p^n%20+%202)%20=%20n)
            * [fast search.sf](./oeis-research/Juri-Stepan%20Gerasimov/Smallest%20prime%20p%20such%20that%20bigomega(p^n%20-%202)%20=%20bigomega(p^n%20+%202)%20=%20n/fast_search.sf)
            * [faster search.sf](./oeis-research/Juri-Stepan%20Gerasimov/Smallest%20prime%20p%20such%20that%20bigomega(p^n%20-%202)%20=%20bigomega(p^n%20+%202)%20=%20n/faster_search.sf)
            * [search.pl](./oeis-research/Juri-Stepan%20Gerasimov/Smallest%20prime%20p%20such%20that%20bigomega(p^n%20-%202)%20=%20bigomega(p^n%20+%202)%20=%20n/search.pl)
            * [simple prog.sf](./oeis-research/Juri-Stepan%20Gerasimov/Smallest%20prime%20p%20such%20that%20bigomega(p^n%20-%202)%20=%20bigomega(p^n%20+%202)%20=%20n/simple_prog.sf)
        * [Smallest prime p such that omega(p^n - 1) is equal to n](./oeis-research/Juri-Stepan%20Gerasimov/Smallest%20prime%20p%20such%20that%20omega(p^n%20-%201)%20is%20equal%20to%20n)
            * [explicit is omega prime.sf](./oeis-research/Juri-Stepan%20Gerasimov/Smallest%20prime%20p%20such%20that%20omega(p^n%20-%201)%20is%20equal%20to%20n/explicit_is_omega_prime.sf)
            * [prog.sf](./oeis-research/Juri-Stepan%20Gerasimov/Smallest%20prime%20p%20such%20that%20omega(p^n%20-%201)%20is%20equal%20to%20n/prog.sf)
            * [upper-bounds.sf](./oeis-research/Juri-Stepan%20Gerasimov/Smallest%20prime%20p%20such%20that%20omega(p^n%20-%201)%20is%20equal%20to%20n/upper-bounds.sf)
        * [Sum of remainders of the n-th composite mod k, for k=1..n](./oeis-research/Juri-Stepan%20Gerasimov/Sum%20of%20remainders%20of%20the%20n-th%20composite%20mod%20k,%20for%20k=1..n)
            * [prog.sf](./oeis-research/Juri-Stepan%20Gerasimov/Sum%20of%20remainders%20of%20the%20n-th%20composite%20mod%20k,%20for%20k=1..n/prog.sf)
    * [Kelvin Voskuijl](./oeis-research/Kelvin%20Voskuijl)
        * [Numbers that are both k-gonal and (k+1)-gonal for some k >= 3](./oeis-research/Kelvin%20Voskuijl/Numbers%20that%20are%20both%20k-gonal%20and%20(k+1)-gonal%20for%20some%20k%20>=%203)
            * [prog.sf](./oeis-research/Kelvin%20Voskuijl/Numbers%20that%20are%20both%20k-gonal%20and%20(k+1)-gonal%20for%20some%20k%20>=%203/prog.sf)
            * [solve.sf](./oeis-research/Kelvin%20Voskuijl/Numbers%20that%20are%20both%20k-gonal%20and%20(k+1)-gonal%20for%20some%20k%20>=%203/solve.sf)
        * [Numbers that are simultaneously k-gonal and k-gonal pyramidal for some k >= 3](./oeis-research/Kelvin%20Voskuijl/Numbers%20that%20are%20simultaneously%20k-gonal%20and%20k-gonal%20pyramidal%20for%20some%20k%20>=%203)
            * [solve.sf](./oeis-research/Kelvin%20Voskuijl/Numbers%20that%20are%20simultaneously%20k-gonal%20and%20k-gonal%20pyramidal%20for%20some%20k%20>=%203/solve.sf)
    * [Kevin Batista](./oeis-research/Kevin%20Batista)
        * [Smallest strong pseudoprime to base 2 with n prime factors](./oeis-research/Kevin%20Batista/Smallest%20strong%20pseudoprime%20to%20base%202%20with%20n%20prime%20factors)
            * [fast prog.pl](./oeis-research/Kevin%20Batista/Smallest%20strong%20pseudoprime%20to%20base%202%20with%20n%20prime%20factors/fast_prog.pl)
            * [prog.sf](./oeis-research/Kevin%20Batista/Smallest%20strong%20pseudoprime%20to%20base%202%20with%20n%20prime%20factors/prog.sf)
            * [prog squarefree.pl](./oeis-research/Kevin%20Batista/Smallest%20strong%20pseudoprime%20to%20base%202%20with%20n%20prime%20factors/prog_squarefree.pl)
            * [slow prog.pl](./oeis-research/Kevin%20Batista/Smallest%20strong%20pseudoprime%20to%20base%202%20with%20n%20prime%20factors/slow_prog.pl)
            * [upper-bounds.pl](./oeis-research/Kevin%20Batista/Smallest%20strong%20pseudoprime%20to%20base%202%20with%20n%20prime%20factors/upper-bounds.pl)
    * [Kevin P. Thompson](./oeis-research/Kevin%20P.%20Thompson)
        * [A(n) is the smallest k > 1 such that k^n + 1 has all prime divisors p == 1 (mod n)](./oeis-research/Kevin%20P.%20Thompson/a(n)%20is%20the%20smallest%20k%20>%201%20such%20that%20k^n%20+%201%20has%20all%20prime%20divisors%20p%20==%201%20(mod%20n))
            * [lower-bounds.sf](./oeis-research/Kevin%20P.%20Thompson/a(n)%20is%20the%20smallest%20k%20>%201%20such%20that%20k^n%20+%201%20has%20all%20prime%20divisors%20p%20==%201%20(mod%20n)/lower-bounds.sf)
        * [Smallest k > 1 such that k^n - 1 is the product of n distinct primes](./oeis-research/Kevin%20P.%20Thompson/Smallest%20k%20>%201%20such%20that%20k^n%20-%201%20is%20the%20product%20of%20n%20distinct%20primes)
            * [is squarefree omega prime.sf](./oeis-research/Kevin%20P.%20Thompson/Smallest%20k%20>%201%20such%20that%20k^n%20-%201%20is%20the%20product%20of%20n%20distinct%20primes/is_squarefree_omega_prime.sf)
            * [prog.sf](./oeis-research/Kevin%20P.%20Thompson/Smallest%20k%20>%201%20such%20that%20k^n%20-%201%20is%20the%20product%20of%20n%20distinct%20primes/prog.sf)
        * [Smallest prime p such that p^(2n-1) - 1 is the product of 2n-1 distinct primes](./oeis-research/Kevin%20P.%20Thompson/Smallest%20prime%20p%20such%20that%20p^(2n-1)%20-%201%20is%20the%20product%20of%202n-1%20distinct%20primes)
            * [is squarefree omega prime.sf](./oeis-research/Kevin%20P.%20Thompson/Smallest%20prime%20p%20such%20that%20p^(2n-1)%20-%201%20is%20the%20product%20of%202n-1%20distinct%20primes/is_squarefree_omega_prime.sf)
            * [prog.sf](./oeis-research/Kevin%20P.%20Thompson/Smallest%20prime%20p%20such%20that%20p^(2n-1)%20-%201%20is%20the%20product%20of%202n-1%20distinct%20primes/prog.sf)
    * [Kevin Ryde](./oeis-research/Kevin%20Ryde)
        * [A(1) = 1 and thereafter a(n) = 2*prime(a(n-1))](./oeis-research/Kevin%20Ryde/a(1)%20=%201%20and%20thereafter%20a(n)%20=%202*prime(a(n-1)))
            * [prog.sf](./oeis-research/Kevin%20Ryde/a(1)%20=%201%20and%20thereafter%20a(n)%20=%202*prime(a(n-1))/prog.sf)
    * [Klaus Brockhaus](./oeis-research/Klaus%20Brockhaus)
        * [Largest prime factor of A096421(n)](./oeis-research/Klaus%20Brockhaus/Largest%20prime%20factor%20of%20A096421(n))
            * [prog.sf](./oeis-research/Klaus%20Brockhaus/Largest%20prime%20factor%20of%20A096421(n)/prog.sf)
        * [Smallest number k such that k-1 and k+1 both have n prime divisors (counted with multiplicity)](./oeis-research/Klaus%20Brockhaus/Smallest%20number%20k%20such%20that%20k-1%20and%20k+1%20both%20have%20n%20prime%20divisors%20(counted%20with%20multiplicity))
            * [generate.pl](./oeis-research/Klaus%20Brockhaus/Smallest%20number%20k%20such%20that%20k-1%20and%20k+1%20both%20have%20n%20prime%20divisors%20(counted%20with%20multiplicity)/generate.pl)
            * [prog ntheory.pl](./oeis-research/Klaus%20Brockhaus/Smallest%20number%20k%20such%20that%20k-1%20and%20k+1%20both%20have%20n%20prime%20divisors%20(counted%20with%20multiplicity)/prog_ntheory.pl)
    * [Labos Elemer](./oeis-research/Labos%20Elemer)
        * [A(n) = tau( sigma n(n) ), where tau is the number of divisors of n](./oeis-research/Labos%20Elemer/a(n)%20=%20tau(%20sigma_n(n)%20),%20where%20tau%20is%20the%20number%20of%20divisors%20of%20n)
            * [prog.sf](./oeis-research/Labos%20Elemer/a(n)%20=%20tau(%20sigma_n(n)%20),%20where%20tau%20is%20the%20number%20of%20divisors%20of%20n/prog.sf)
        * [Index of smallest prime p such that there is a gap of 2^n between p and next prime](./oeis-research/Labos%20Elemer/Index%20of%20smallest%20prime%20p%20such%20that%20there%20is%20a%20gap%20of%202^n%20between%20p%20and%20next%20prime)
            * [prog.pl](./oeis-research/Labos%20Elemer/Index%20of%20smallest%20prime%20p%20such%20that%20there%20is%20a%20gap%20of%202^n%20between%20p%20and%20next%20prime/prog.pl)
        * [Largest prime divisor of n-th primorial + (n+1)-st prime](./oeis-research/Labos%20Elemer/Largest%20prime%20divisor%20of%20n-th%20primorial%20+%20(n+1)-st%20prime)
            * [prog.sf](./oeis-research/Labos%20Elemer/Largest%20prime%20divisor%20of%20n-th%20primorial%20+%20(n+1)-st%20prime/prog.sf)
        * [Least k > 0 such that sigma(factorial(k)) >= n*factorial(k)](./oeis-research/Labos%20Elemer/Least%20k%20>%200%20such%20that%20sigma(factorial(k))%20>=%20n*factorial(k))
            * [binary search.pl](./oeis-research/Labos%20Elemer/Least%20k%20>%200%20such%20that%20sigma(factorial(k))%20>=%20n*factorial(k)/binary_search.pl)
            * [exact.pl](./oeis-research/Labos%20Elemer/Least%20k%20>%200%20such%20that%20sigma(factorial(k))%20>=%20n*factorial(k)/exact.pl)
            * [logs.pl](./oeis-research/Labos%20Elemer/Least%20k%20>%200%20such%20that%20sigma(factorial(k))%20>=%20n*factorial(k)/logs.pl)
        * [Least k such that nextprime(k^n) - prevprime(k^n) = 4](./oeis-research/Labos%20Elemer/Least%20k%20such%20that%20nextprime(k^n)%20-%20prevprime(k^n)%20=%204)
            * [isok.sf](./oeis-research/Labos%20Elemer/Least%20k%20such%20that%20nextprime(k^n)%20-%20prevprime(k^n)%20=%204/isok.sf)
            * [search.pl](./oeis-research/Labos%20Elemer/Least%20k%20such%20that%20nextprime(k^n)%20-%20prevprime(k^n)%20=%204/search.pl)
            * [sort primes.sf](./oeis-research/Labos%20Elemer/Least%20k%20such%20that%20nextprime(k^n)%20-%20prevprime(k^n)%20=%204/sort_primes.sf)
        * [Number of different terms in the period of sqrt cfrac of repunits](./oeis-research/Labos%20Elemer/Number%20of%20different%20terms%20in%20the%20period%20of%20sqrt%20cfrac%20of%20repunits)
            * [prog.pl](./oeis-research/Labos%20Elemer/Number%20of%20different%20terms%20in%20the%20period%20of%20sqrt%20cfrac%20of%20repunits/prog.pl)
        * [Number of nonsquarefree numbers not exceeding n](./oeis-research/Labos%20Elemer/Number%20of%20nonsquarefree%20numbers%20not%20exceeding%20n)
            * [prog.sf](./oeis-research/Labos%20Elemer/Number%20of%20nonsquarefree%20numbers%20not%20exceeding%20n/prog.sf)
        * [Number of powerful numbers between 2^(n-1)+1 and 2^n](./oeis-research/Labos%20Elemer/Number%20of%20powerful%20numbers%20between%202^(n-1)+1%20and%202^n)
            * [prog.pl](./oeis-research/Labos%20Elemer/Number%20of%20powerful%20numbers%20between%202^(n-1)+1%20and%202^n/prog.pl)
            * [prog faster.sf](./oeis-research/Labos%20Elemer/Number%20of%20powerful%20numbers%20between%202^(n-1)+1%20and%202^n/prog_faster.sf)
        * [Numbers k such that Cyclotomic(k,k) is prime](./oeis-research/Labos%20Elemer/Numbers%20k%20such%20that%20Cyclotomic(k,k)%20is%20prime)
            * [prog.sf](./oeis-research/Labos%20Elemer/Numbers%20k%20such%20that%20Cyclotomic(k,k)%20is%20prime/prog.sf)
            * [prog2.sf](./oeis-research/Labos%20Elemer/Numbers%20k%20such%20that%20Cyclotomic(k,k)%20is%20prime/prog2.sf)
        * [Smallest x such that prime(x) mod composite(x) = n](./oeis-research/Labos%20Elemer/Smallest%20x%20such%20that%20prime(x)%20mod%20composite(x)%20=%20n)
            * [prog.pl](./oeis-research/Labos%20Elemer/Smallest%20x%20such%20that%20prime(x)%20mod%20composite(x)%20=%20n/prog.pl)
    * [Lekraj Beedassy](./oeis-research/Lekraj%20Beedassy)
        * [LCM primes](./oeis-research/Lekraj%20Beedassy/LCM%20primes)
            * [lcm p minus 1.sf](./oeis-research/Lekraj%20Beedassy/LCM%20primes/lcm_p_minus_1.sf)
            * [lcm p plus 1.sf](./oeis-research/Lekraj%20Beedassy/LCM%20primes/lcm_p_plus_1.sf)
        * [Primes p such that consecutive lcm +- 1 is prime](./oeis-research/Lekraj%20Beedassy/Primes%20p%20such%20that%20consecutive%20lcm%20+-%201%20is%20prime)
            * [prog.sf](./oeis-research/Lekraj%20Beedassy/Primes%20p%20such%20that%20consecutive%20lcm%20+-%201%20is%20prime/prog.sf)
        * [Smallest number m with n ones in sqrt cfrac expansion](./oeis-research/Lekraj%20Beedassy/Smallest%20number%20m%20with%20n%20ones%20in%20sqrt%20cfrac%20expansion)
            * [generate from cfrac.sf](./oeis-research/Lekraj%20Beedassy/Smallest%20number%20m%20with%20n%20ones%20in%20sqrt%20cfrac%20expansion/generate_from_cfrac.sf)
            * [prog.sf](./oeis-research/Lekraj%20Beedassy/Smallest%20number%20m%20with%20n%20ones%20in%20sqrt%20cfrac%20expansion/prog.sf)
        * [Smallest prime p such that p+1 is the product of exactly n distinct prime numbers](./oeis-research/Lekraj%20Beedassy/Smallest%20prime%20p%20such%20that%20p+1%20is%20the%20product%20of%20exactly%20n%20distinct%20prime%20numbers)
            * [prog.sf](./oeis-research/Lekraj%20Beedassy/Smallest%20prime%20p%20such%20that%20p+1%20is%20the%20product%20of%20exactly%20n%20distinct%20prime%20numbers/prog.sf)
        * [Smallest prime p such that the Mersenne number A000225(p) = 2^p - 1 has exactly n prime factors (counted with multiplicity)](./oeis-research/Lekraj%20Beedassy/Smallest%20prime%20p%20such%20that%20the%20Mersenne%20number%20A000225(p)%20=%202^p%20-%201%20has%20exactly%20n%20prime%20factors%20(counted%20with%20multiplicity))
            * [prog.sf](./oeis-research/Lekraj%20Beedassy/Smallest%20prime%20p%20such%20that%20the%20Mersenne%20number%20A000225(p)%20=%202^p%20-%201%20has%20exactly%20n%20prime%20factors%20(counted%20with%20multiplicity)/prog.sf)
    * [Leroy Quet](./oeis-research/Leroy%20Quet)
        * [Mobius transform of Sum {k=1..n} tau(k)](./oeis-research/Leroy%20Quet/Mobius%20transform%20of%20Sum_{k=1..n}%20tau(k))
            * [prog.sf](./oeis-research/Leroy%20Quet/Mobius%20transform%20of%20Sum_{k=1..n}%20tau(k)/prog.sf)
    * [Lorenzo Sauras Altuzarra](./oeis-research/Lorenzo%20Sauras%20Altuzarra)
        * [Inverse tetrahedral](./oeis-research/Lorenzo%20Sauras%20Altuzarra/Inverse%20tetrahedral)
            * [prog.sf](./oeis-research/Lorenzo%20Sauras%20Altuzarra/Inverse%20tetrahedral/prog.sf)
    * [Luis H. Gallardo](./oeis-research/Luis%20H.%20Gallardo)
        * [Number of distinct prime factors of g(p) = (p^p-1) over (p-1) where p = prime(n)](./oeis-research/Luis%20H.%20Gallardo/Number%20of%20distinct%20prime%20factors%20of%20g(p)%20=%20(p^p-1)%20over%20(p-1)%20where%20p%20=%20prime(n))
            * [prog.sf](./oeis-research/Luis%20H.%20Gallardo/Number%20of%20distinct%20prime%20factors%20of%20g(p)%20=%20(p^p-1)%20over%20(p-1)%20where%20p%20=%20prime(n)/prog.sf)
    * [M. F. Hasler](./oeis-research/M.%20F.%20Hasler)
        * [Highly composite numbers - twin primes](./oeis-research/M.%20F.%20Hasler/Highly%20composite%20numbers%20-%20twin%20primes)
            * [hcn.pl](./oeis-research/M.%20F.%20Hasler/Highly%20composite%20numbers%20-%20twin%20primes/hcn.pl)
            * [hcn between twin primes.pl](./oeis-research/M.%20F.%20Hasler/Highly%20composite%20numbers%20-%20twin%20primes/hcn_between_twin_primes.pl)
        * [Indices of Tribonacci primes](./oeis-research/M.%20F.%20Hasler/Indices%20of%20Tribonacci%20primes)
            * [prog.pl](./oeis-research/M.%20F.%20Hasler/Indices%20of%20Tribonacci%20primes/prog.pl)
        * [Largest prime factor of A001008(n), numerator of n-th harmonic number](./oeis-research/M.%20F.%20Hasler/Largest%20prime%20factor%20of%20A001008(n),%20numerator%20of%20n-th%20harmonic%20number)
            * [prog.sf](./oeis-research/M.%20F.%20Hasler/Largest%20prime%20factor%20of%20A001008(n),%20numerator%20of%20n-th%20harmonic%20number/prog.sf)
        * [Least odd primitive abundant number with n prime factors, counted with multiplicity](./oeis-research/M.%20F.%20Hasler/Least%20odd%20primitive%20abundant%20number%20with%20n%20prime%20factors,%20counted%20with%20multiplicity)
            * [generate.pl](./oeis-research/M.%20F.%20Hasler/Least%20odd%20primitive%20abundant%20number%20with%20n%20prime%20factors,%20counted%20with%20multiplicity/generate.pl)
        * [Numbers k such that Omega(k) = Omega(2^k-1), where Omega(k) is the number of prime factors of k counted with multiplicity (A001222)](./oeis-research/M.%20F.%20Hasler/Numbers%20k%20such%20that%20Omega(k)%20=%20Omega(2^k-1),%20where%20Omega(k)%20is%20the%20number%20of%20prime%20factors%20of%20k%20counted%20with%20multiplicity%20(A001222))
            * [prog.sf](./oeis-research/M.%20F.%20Hasler/Numbers%20k%20such%20that%20Omega(k)%20=%20Omega(2^k-1),%20where%20Omega(k)%20is%20the%20number%20of%20prime%20factors%20of%20k%20counted%20with%20multiplicity%20(A001222)/prog.sf)
        * [Numbers of the form N = a+b+c such that N^3 = concat(a,b,c)](./oeis-research/M.%20F.%20Hasler/Numbers%20of%20the%20form%20N%20=%20a+b+c%20such%20that%20N^3%20=%20concat(a,b,c))
            * [prog.pl](./oeis-research/M.%20F.%20Hasler/Numbers%20of%20the%20form%20N%20=%20a+b+c%20such%20that%20N^3%20=%20concat(a,b,c)/prog.pl)
            * [prog.sf](./oeis-research/M.%20F.%20Hasler/Numbers%20of%20the%20form%20N%20=%20a+b+c%20such%20that%20N^3%20=%20concat(a,b,c)/prog.sf)
        * [Sum of sigma(n) mod k for k = 1..n-1](./oeis-research/M.%20F.%20Hasler/Sum%20of%20sigma(n)%20mod%20k%20for%20k%20=%201..n-1)
            * [prog.sf](./oeis-research/M.%20F.%20Hasler/Sum%20of%20sigma(n)%20mod%20k%20for%20k%20=%201..n-1/prog.sf)
    * [M. Farrokhi D. G.](./oeis-research/M.%20Farrokhi%20D.%20G.)
        * [Primes p such that (2^(p-1)*(p+1) - 1) div p is prime](./oeis-research/M.%20Farrokhi%20D.%20G./Primes%20p%20such%20that%20(2^(p-1)*(p+1)%20-%201)%20div%20p%20is%20prime)
            * [prog.sf](./oeis-research/M.%20Farrokhi%20D.%20G./Primes%20p%20such%20that%20(2^(p-1)*(p+1)%20-%201)%20div%20p%20is%20prime/prog.sf)
    * [Maheswara Rao Valluri](./oeis-research/Maheswara%20Rao%20Valluri)
        * [Glitch primes](./oeis-research/Maheswara%20Rao%20Valluri/Glitch%20primes)
            * [prog.pl](./oeis-research/Maheswara%20Rao%20Valluri/Glitch%20primes/prog.pl)
            * [prog2.pl](./oeis-research/Maheswara%20Rao%20Valluri/Glitch%20primes/prog2.pl)
            * [prog3.pl](./oeis-research/Maheswara%20Rao%20Valluri/Glitch%20primes/prog3.pl)
    * [Manuel Valdivia](./oeis-research/Manuel%20Valdivia)
        * [Smallest prime p such that 2^(p-1) == 1 mod prod a(k)](./oeis-research/Manuel%20Valdivia/Smallest%20prime%20p%20such%20that%202^(p-1)%20==%201%20mod%20prod%20a(k))
            * [prog.pl](./oeis-research/Manuel%20Valdivia/Smallest%20prime%20p%20such%20that%202^(p-1)%20==%201%20mod%20prod%20a(k)/prog.pl)
    * [Marco Ripà](./oeis-research/Marco%20Ripà)
        * [Initial digit of 2^(2^n) (A001146(n))](./oeis-research/Marco%20Ripà/Initial%20digit%20of%202^(2^n)%20(A001146(n)))
            * [prog.sf](./oeis-research/Marco%20Ripà/Initial%20digit%20of%202^(2^n)%20(A001146(n))/prog.sf)
        * [Initial digit of n^((n + 1)^(n + 2))](./oeis-research/Marco%20Ripà/Initial%20digit%20of%20n^((n%20+%201)^(n%20+%202)))
            * [prog.sf](./oeis-research/Marco%20Ripà/Initial%20digit%20of%20n^((n%20+%201)^(n%20+%202))/prog.sf)
    * [Marius A. Burtea](./oeis-research/Marius%20A.%20Burtea)
        * [Triangular numbers whose arithmetic derivative is also a triangular number](./oeis-research/Marius%20A.%20Burtea/Triangular%20numbers%20whose%20arithmetic%20derivative%20is%20also%20a%20triangular%20number)
            * [prog.pl](./oeis-research/Marius%20A.%20Burtea/Triangular%20numbers%20whose%20arithmetic%20derivative%20is%20also%20a%20triangular%20number/prog.pl)
    * [Matthew Campbell](./oeis-research/Matthew%20Campbell)
        * [A(n) is obtained by applying the map k -> composite(k) n times, starting at n](./oeis-research/Matthew%20Campbell/a(n)%20is%20obtained%20by%20applying%20the%20map%20k%20->%20composite(k)%20n%20times,%20starting%20at%20n)
            * [prog.sf](./oeis-research/Matthew%20Campbell/a(n)%20is%20obtained%20by%20applying%20the%20map%20k%20->%20composite(k)%20n%20times,%20starting%20at%20n/prog.sf)
    * [Max Alekseyev](./oeis-research/Max%20Alekseyev)
        * [Base-2 pseudoprimes of the form 2*p*q where p and q are primes](./oeis-research/Max%20Alekseyev/Base-2%20pseudoprimes%20of%20the%20form%202*p*q%20where%20p%20and%20q%20are%20primes)
            * [prog.pl](./oeis-research/Max%20Alekseyev/Base-2%20pseudoprimes%20of%20the%20form%202*p*q%20where%20p%20and%20q%20are%20primes/prog.pl)
            * [prog mpz.pl](./oeis-research/Max%20Alekseyev/Base-2%20pseudoprimes%20of%20the%20form%202*p*q%20where%20p%20and%20q%20are%20primes/prog_mpz.pl)
        * [Numbers m such that both m and 2m+1 are Fermat pseudoprimes base 2](./oeis-research/Max%20Alekseyev/Numbers%20m%20such%20that%20both%20m%20and%202m+1%20are%20Fermat%20pseudoprimes%20base%202)
            * [prog.pl](./oeis-research/Max%20Alekseyev/Numbers%20m%20such%20that%20both%20m%20and%202m+1%20are%20Fermat%20pseudoprimes%20base%202/prog.pl)
    * [Max Z. Scialabba](./oeis-research/Max%20Z.%20Scialabba)
        * [Least number k such that sigma(sigma(k) * k) > n * sigma(k) * k](./oeis-research/Max%20Z.%20Scialabba/Least%20number%20k%20such%20that%20sigma(sigma(k)%20*%20k)%20>%20n%20*%20sigma(k)%20*%20k)
            * [upper-bounds.pl](./oeis-research/Max%20Z.%20Scialabba/Least%20number%20k%20such%20that%20sigma(sigma(k)%20*%20k)%20>%20n%20*%20sigma(k)%20*%20k/upper-bounds.pl)
    * [Metin Sariyar](./oeis-research/Metin%20Sariyar)
        * [Numbers k such that (prime(k) + composite(k)) == 0 (mod k)](./oeis-research/Metin%20Sariyar/Numbers%20k%20such%20that%20(prime(k)%20+%20composite(k))%20==%200%20(mod%20k))
            * [binary search.sf](./oeis-research/Metin%20Sariyar/Numbers%20k%20such%20that%20(prime(k)%20+%20composite(k))%20==%200%20(mod%20k)/binary_search.sf)
            * [nearby search.pl](./oeis-research/Metin%20Sariyar/Numbers%20k%20such%20that%20(prime(k)%20+%20composite(k))%20==%200%20(mod%20k)/nearby_search.pl)
            * [prog.pl](./oeis-research/Metin%20Sariyar/Numbers%20k%20such%20that%20(prime(k)%20+%20composite(k))%20==%200%20(mod%20k)/prog.pl)
        * [Numbers k such that sigma(k) = factorial of sum of digits of k](./oeis-research/Metin%20Sariyar/Numbers%20k%20such%20that%20sigma(k)%20=%20factorial%20of%20sum%20of%20digits%20of%20k)
            * [prog.pl](./oeis-research/Metin%20Sariyar/Numbers%20k%20such%20that%20sigma(k)%20=%20factorial%20of%20sum%20of%20digits%20of%20k/prog.pl)
        * [Numbers k such that the decimal expansion of the k-th harmonic number starts with the digits of k](./oeis-research/Metin%20Sariyar/Numbers%20k%20such%20that%20the%20decimal%20expansion%20of%20the%20k-th%20harmonic%20number%20starts%20with%20the%20digits%20of%20k)
            * [binary search.sf](./oeis-research/Metin%20Sariyar/Numbers%20k%20such%20that%20the%20decimal%20expansion%20of%20the%20k-th%20harmonic%20number%20starts%20with%20the%20digits%20of%20k/binary_search.sf)
        * [Numbers m such that Sum {k=1..m} omega(k) = sigma(m)](./oeis-research/Metin%20Sariyar/Numbers%20m%20such%20that%20Sum_{k=1..m}%20omega(k)%20=%20sigma(m))
            * [inverse sigma smooth search.pl](./oeis-research/Metin%20Sariyar/Numbers%20m%20such%20that%20Sum_{k=1..m}%20omega(k)%20=%20sigma(m)/inverse_sigma_smooth_search.pl)
            * [smooth search.pl](./oeis-research/Metin%20Sariyar/Numbers%20m%20such%20that%20Sum_{k=1..m}%20omega(k)%20=%20sigma(m)/smooth_search.pl)
        * [Numbers n such that sum of first k composites k^k is prime](./oeis-research/Metin%20Sariyar/Numbers%20n%20such%20that%20sum%20of%20first%20k%20composites%20k^k%20is%20prime)
            * [prog.sf](./oeis-research/Metin%20Sariyar/Numbers%20n%20such%20that%20sum%20of%20first%20k%20composites%20k^k%20is%20prime/prog.sf)
        * [Start of the first run of n consecutive primes using only prime digits](./oeis-research/Metin%20Sariyar/Start%20of%20the%20first%20run%20of%20n%20consecutive%20primes%20using%20only%20prime%20digits)
            * [prog.pl](./oeis-research/Metin%20Sariyar/Start%20of%20the%20first%20run%20of%20n%20consecutive%20primes%20using%20only%20prime%20digits/prog.pl)
        * [Sum of first n prime powers of 2 + prime(n+1) is prime](./oeis-research/Metin%20Sariyar/Sum%20of%20first%20n%20prime%20powers%20of%202%20+%20prime(n+1)%20is%20prime)
            * [prog.sf](./oeis-research/Metin%20Sariyar/Sum%20of%20first%20n%20prime%20powers%20of%202%20+%20prime(n+1)%20is%20prime/prog.sf)
        * [Twin prime and prime-indices emirps](./oeis-research/Metin%20Sariyar/Twin%20prime%20and%20prime-indices%20emirps)
            * [prog.pl](./oeis-research/Metin%20Sariyar/Twin%20prime%20and%20prime-indices%20emirps/prog.pl)
    * [Michael De Vlieger](./oeis-research/Michael%20De%20Vlieger)
        * [Largest prime(n)-smooth k < primorial(n+1), where primorial = A002110](./oeis-research/Michael%20De%20Vlieger/Largest%20prime(n)-smooth%20k%20<%20primorial(n+1),%20where%20primorial%20=%20A002110)
            * [prog.sf](./oeis-research/Michael%20De%20Vlieger/Largest%20prime(n)-smooth%20k%20<%20primorial(n+1),%20where%20primorial%20=%20A002110/prog.sf)
        * [Smallest prime(n)-smooth k > primorial(n+1), where primorial = A002110](./oeis-research/Michael%20De%20Vlieger/Smallest%20prime(n)-smooth%20k%20>%20primorial(n+1),%20where%20primorial%20=%20A002110)
            * [prog.sf](./oeis-research/Michael%20De%20Vlieger/Smallest%20prime(n)-smooth%20k%20>%20primorial(n+1),%20where%20primorial%20=%20A002110/prog.sf)
    * [Michael S. Branicky](./oeis-research/Michael%20S.%20Branicky)
        * [Least number ending in at least n identical digits that has exactly n distinct prime divisors](./oeis-research/Michael%20S.%20Branicky/Least%20number%20ending%20in%20at%20least%20n%20identical%20digits%20that%20has%20exactly%20n%20distinct%20prime%20divisors)
            * [prog.pl](./oeis-research/Michael%20S.%20Branicky/Least%20number%20ending%20in%20at%20least%20n%20identical%20digits%20that%20has%20exactly%20n%20distinct%20prime%20divisors/prog.pl)
            * [prog.sf](./oeis-research/Michael%20S.%20Branicky/Least%20number%20ending%20in%20at%20least%20n%20identical%20digits%20that%20has%20exactly%20n%20distinct%20prime%20divisors/prog.sf)
            * [prog bigint.pl](./oeis-research/Michael%20S.%20Branicky/Least%20number%20ending%20in%20at%20least%20n%20identical%20digits%20that%20has%20exactly%20n%20distinct%20prime%20divisors/prog_bigint.pl)
        * [Smallest palindrome with exactly n distinct prime factors](./oeis-research/Michael%20S.%20Branicky/Smallest%20palindrome%20with%20exactly%20n%20distinct%20prime%20factors)
            * [michael omega palindromes.py](./oeis-research/Michael%20S.%20Branicky/Smallest%20palindrome%20with%20exactly%20n%20distinct%20prime%20factors/michael_omega_palindromes.py)
            * [omega palindromes.jl](./oeis-research/Michael%20S.%20Branicky/Smallest%20palindrome%20with%20exactly%20n%20distinct%20prime%20factors/omega_palindromes.jl)
            * [omega palindromes.pl](./oeis-research/Michael%20S.%20Branicky/Smallest%20palindrome%20with%20exactly%20n%20distinct%20prime%20factors/omega_palindromes.pl)
            * [prog.sf](./oeis-research/Michael%20S.%20Branicky/Smallest%20palindrome%20with%20exactly%20n%20distinct%20prime%20factors/prog.sf)
    * [Michel Lagneau](./oeis-research/Michel%20Lagneau)
        * [Least k such that prime(k) + prime(k+1) contains n prime divisors](./oeis-research/Michel%20Lagneau/Least%20k%20such%20that%20prime(k)%20+%20prime(k+1)%20contains%20n%20prime%20divisors)
            * [prog.pl](./oeis-research/Michel%20Lagneau/Least%20k%20such%20that%20prime(k)%20+%20prime(k+1)%20contains%20n%20prime%20divisors/prog.pl)
        * [Numbers k such that sigma 2(Fibonacci(k)^2 + 1) == 0 (mod Fibonacci(k))](./oeis-research/Michel%20Lagneau/Numbers%20k%20such%20that%20sigma_2(Fibonacci(k)^2%20+%201)%20==%200%20(mod%20Fibonacci(k)))
            * [prog.sf](./oeis-research/Michel%20Lagneau/Numbers%20k%20such%20that%20sigma_2(Fibonacci(k)^2%20+%201)%20==%200%20(mod%20Fibonacci(k))/prog.sf)
        * [Semiprimes p-q is divisilbe by 2^n](./oeis-research/Michel%20Lagneau/Semiprimes%20p-q%20is%20divisilbe%20by%202^n)
            * [verify.sf](./oeis-research/Michel%20Lagneau/Semiprimes%20p-q%20is%20divisilbe%20by%202^n/verify.sf)
            * [x.pl](./oeis-research/Michel%20Lagneau/Semiprimes%20p-q%20is%20divisilbe%20by%202^n/x.pl)
            * [x2.pl](./oeis-research/Michel%20Lagneau/Semiprimes%20p-q%20is%20divisilbe%20by%202^n/x2.pl)
        * [Smallest number k such that k and k+1 are both of the form p*q^n where p and q are distinct primes](./oeis-research/Michel%20Lagneau/Smallest%20number%20k%20such%20that%20k%20and%20k+1%20are%20both%20of%20the%20form%20p*q^n%20where%20p%20and%20q%20are%20distinct%20primes)
            * [upper-bounds.sf](./oeis-research/Michel%20Lagneau/Smallest%20number%20k%20such%20that%20k%20and%20k+1%20are%20both%20of%20the%20form%20p*q^n%20where%20p%20and%20q%20are%20distinct%20primes/upper-bounds.sf)
        * [Smallest number k such that k^n + 1 contains n distinct prime divisors](./oeis-research/Michel%20Lagneau/Smallest%20number%20k%20such%20that%20k^n%20+%201%20contains%20n%20distinct%20prime%20divisors)
            * [is omega prime.sf](./oeis-research/Michel%20Lagneau/Smallest%20number%20k%20such%20that%20k^n%20+%201%20contains%20n%20distinct%20prime%20divisors/is_omega_prime.sf)
            * [prog.sf](./oeis-research/Michel%20Lagneau/Smallest%20number%20k%20such%20that%20k^n%20+%201%20contains%20n%20distinct%20prime%20divisors/prog.sf)
            * [upper bounds.sf](./oeis-research/Michel%20Lagneau/Smallest%20number%20k%20such%20that%20k^n%20+%201%20contains%20n%20distinct%20prime%20divisors/upper_bounds.sf)
        * [Smallest number such that k^2 + 1 has n distinct prime factors](./oeis-research/Michel%20Lagneau/Smallest%20number%20such%20that%20k^2%20+%201%20has%20n%20distinct%20prime%20factors)
            * [prog.pl](./oeis-research/Michel%20Lagneau/Smallest%20number%20such%20that%20k^2%20+%201%20has%20n%20distinct%20prime%20factors/prog.pl)
            * [prog.sf](./oeis-research/Michel%20Lagneau/Smallest%20number%20such%20that%20k^2%20+%201%20has%20n%20distinct%20prime%20factors/prog.sf)
            * [prog squarefree.pl](./oeis-research/Michel%20Lagneau/Smallest%20number%20such%20that%20k^2%20+%201%20has%20n%20distinct%20prime%20factors/prog_squarefree.pl)
        * [Smallest number such that k^n - 1 contains n distinct prime divisors](./oeis-research/Michel%20Lagneau/Smallest%20number%20such%20that%20k^n%20-%201%20contains%20n%20distinct%20prime%20divisors)
            * [is omega prime.sf](./oeis-research/Michel%20Lagneau/Smallest%20number%20such%20that%20k^n%20-%201%20contains%20n%20distinct%20prime%20divisors/is_omega_prime.sf)
            * [prog.sf](./oeis-research/Michel%20Lagneau/Smallest%20number%20such%20that%20k^n%20-%201%20contains%20n%20distinct%20prime%20divisors/prog.sf)
        * [Smallest prime factor of p^p - 1 that is congruent to 1 modulo p where p = prime(n)](./oeis-research/Michel%20Lagneau/Smallest%20prime%20factor%20of%20p^p%20-%201%20that%20is%20congruent%20to%201%20modulo%20p%20where%20p%20=%20prime(n))
            * [prog.sf](./oeis-research/Michel%20Lagneau/Smallest%20prime%20factor%20of%20p^p%20-%201%20that%20is%20congruent%20to%201%20modulo%20p%20where%20p%20=%20prime(n)/prog.sf)
    * [Michel Marcus](./oeis-research/Michel%20Marcus)
        * [A(n) is the least integer m such that M(m) is divisible by prime(n)^2 or -1 if no such m exists](./oeis-research/Michel%20Marcus/a(n)%20is%20the%20least%20integer%20m%20such%20that%20M(m)%20is%20divisible%20by%20prime(n)^2%20or%20-1%20if%20no%20such%20m%20exists)
            * [prog.sf](./oeis-research/Michel%20Marcus/a(n)%20is%20the%20least%20integer%20m%20such%20that%20M(m)%20is%20divisible%20by%20prime(n)^2%20or%20-1%20if%20no%20such%20m%20exists/prog.sf)
        * [Exponents d of powers of 2, q, such that each of q-1 and q+1 are either a power of prime or a semiprime](./oeis-research/Michel%20Marcus/Exponents%20d%20of%20powers%20of%202,%20q,%20such%20that%20each%20of%20q-1%20and%20q+1%20are%20either%20a%20power%20of%20prime%20or%20a%20semiprime)
            * [prog.sf](./oeis-research/Michel%20Marcus/Exponents%20d%20of%20powers%20of%202,%20q,%20such%20that%20each%20of%20q-1%20and%20q+1%20are%20either%20a%20power%20of%20prime%20or%20a%20semiprime/prog.sf)
        * [Integers k such that A110299(k) is prime](./oeis-research/Michel%20Marcus/Integers%20k%20such%20that%20A110299(k)%20is%20prime)
            * [prog.sf](./oeis-research/Michel%20Marcus/Integers%20k%20such%20that%20A110299(k)%20is%20prime/prog.sf)
        * [Integers m such that m and m+1 are terms of A111035](./oeis-research/Michel%20Marcus/Integers%20m%20such%20that%20m%20and%20m+1%20are%20terms%20of%20A111035)
            * [prog.pl](./oeis-research/Michel%20Marcus/Integers%20m%20such%20that%20m%20and%20m+1%20are%20terms%20of%20A111035/prog.pl)
        * [Least integer k such that the inverse of sum of inv(phi(k+j)) for j=1..n is an integer](./oeis-research/Michel%20Marcus/Least%20integer%20k%20such%20that%20the%20inverse%20of%20sum%20of%20inv(phi(k+j))%20for%20j=1..n%20is%20an%20integer)
            * [prog.sf](./oeis-research/Michel%20Marcus/Least%20integer%20k%20such%20that%20the%20inverse%20of%20sum%20of%20inv(phi(k+j))%20for%20j=1..n%20is%20an%20integer/prog.sf)
        * [Least Lucas number with n Lucas divisors](./oeis-research/Michel%20Marcus/Least%20Lucas%20number%20with%20n%20Lucas%20divisors)
            * [faster prog.sf](./oeis-research/Michel%20Marcus/Least%20Lucas%20number%20with%20n%20Lucas%20divisors/faster_prog.sf)
            * [prog.sf](./oeis-research/Michel%20Marcus/Least%20Lucas%20number%20with%20n%20Lucas%20divisors/prog.sf)
        * [Least number k such that the concatenation of k composites from composite(n) is prime](./oeis-research/Michel%20Marcus/Least%20number%20k%20such%20that%20the%20concatenation%20of%20k%20composites%20from%20composite(n)%20is%20prime)
            * [prog.sf](./oeis-research/Michel%20Marcus/Least%20number%20k%20such%20that%20the%20concatenation%20of%20k%20composites%20from%20composite(n)%20is%20prime/prog.sf)
        * [Number of Lucas divisors of the n-th Lucas number](./oeis-research/Michel%20Marcus/Number%20of%20Lucas%20divisors%20of%20the%20n-th%20Lucas%20number)
            * [prog.sf](./oeis-research/Michel%20Marcus/Number%20of%20Lucas%20divisors%20of%20the%20n-th%20Lucas%20number/prog.sf)
        * [Prime p for which the continued fraction expansion of sqrt(p) has exactly n consecutive 1's starting at position 2](./oeis-research/Michel%20Marcus/Prime%20p%20for%20which%20the%20continued%20fraction%20expansion%20of%20sqrt(p)%20has%20exactly%20n%20consecutive%201's%20starting%20at%20position%202)
            * [prog.pl](./oeis-research/Michel%20Marcus/Prime%20p%20for%20which%20the%20continued%20fraction%20expansion%20of%20sqrt(p)%20has%20exactly%20n%20consecutive%201's%20starting%20at%20position%202/prog.pl)
            * [r.pl](./oeis-research/Michel%20Marcus/Prime%20p%20for%20which%20the%20continued%20fraction%20expansion%20of%20sqrt(p)%20has%20exactly%20n%20consecutive%201's%20starting%20at%20position%202/r.pl)
        * [Primes p such that the greatest common divisor of 2^p+1 and 3^p+1 is composite](./oeis-research/Michel%20Marcus/Primes%20p%20such%20that%20the%20greatest%20common%20divisor%20of%202^p+1%20and%203^p+1%20is%20composite)
            * [check.sf](./oeis-research/Michel%20Marcus/Primes%20p%20such%20that%20the%20greatest%20common%20divisor%20of%202^p+1%20and%203^p+1%20is%20composite/check.sf)
            * [from psp.pl](./oeis-research/Michel%20Marcus/Primes%20p%20such%20that%20the%20greatest%20common%20divisor%20of%202^p+1%20and%203^p+1%20is%20composite/from_psp.pl)
            * [search.pl](./oeis-research/Michel%20Marcus/Primes%20p%20such%20that%20the%20greatest%20common%20divisor%20of%202^p+1%20and%203^p+1%20is%20composite/search.pl)
            * [search.sf](./oeis-research/Michel%20Marcus/Primes%20p%20such%20that%20the%20greatest%20common%20divisor%20of%202^p+1%20and%203^p+1%20is%20composite/search.sf)
        * [Primes where every 0-splitting is prime](./oeis-research/Michel%20Marcus/Primes%20where%20every%200-splitting%20is%20prime)
            * [generalization to other bases.sf](./oeis-research/Michel%20Marcus/Primes%20where%20every%200-splitting%20is%20prime/generalization_to_other_bases.sf)
            * [prog.pl](./oeis-research/Michel%20Marcus/Primes%20where%20every%200-splitting%20is%20prime/prog.pl)
            * [sort terms.sf](./oeis-research/Michel%20Marcus/Primes%20where%20every%200-splitting%20is%20prime/sort_terms.sf)
            * [y.pl](./oeis-research/Michel%20Marcus/Primes%20where%20every%200-splitting%20is%20prime/y.pl)
            * [z.pl](./oeis-research/Michel%20Marcus/Primes%20where%20every%200-splitting%20is%20prime/z.pl)
        * [Smallest m such that gcd of the x's that satisfy sigma(x) = m is n](./oeis-research/Michel%20Marcus/Smallest%20m%20such%20that%20gcd%20of%20the%20x's%20that%20satisfy%20sigma(x)%20=%20m%20is%20n)
            * [comb.sf](./oeis-research/Michel%20Marcus/Smallest%20m%20such%20that%20gcd%20of%20the%20x's%20that%20satisfy%20sigma(x)%20=%20m%20is%20n/comb.sf)
            * [search.pl](./oeis-research/Michel%20Marcus/Smallest%20m%20such%20that%20gcd%20of%20the%20x's%20that%20satisfy%20sigma(x)%20=%20m%20is%20n/search.pl)
            * [smooth generate.pl](./oeis-research/Michel%20Marcus/Smallest%20m%20such%20that%20gcd%20of%20the%20x's%20that%20satisfy%20sigma(x)%20=%20m%20is%20n/smooth_generate.pl)
            * [sort upperbounds.sf](./oeis-research/Michel%20Marcus/Smallest%20m%20such%20that%20gcd%20of%20the%20x's%20that%20satisfy%20sigma(x)%20=%20m%20is%20n/sort_upperbounds.sf)
        * [Smallest m such that the m-th Lucas number has exactly n divisors that are also Lucas numbers](./oeis-research/Michel%20Marcus/Smallest%20m%20such%20that%20the%20m-th%20Lucas%20number%20has%20exactly%20n%20divisors%20that%20are%20also%20Lucas%20numbers)
            * [prog.pl](./oeis-research/Michel%20Marcus/Smallest%20m%20such%20that%20the%20m-th%20Lucas%20number%20has%20exactly%20n%20divisors%20that%20are%20also%20Lucas%20numbers/prog.pl)
            * [prog.sf](./oeis-research/Michel%20Marcus/Smallest%20m%20such%20that%20the%20m-th%20Lucas%20number%20has%20exactly%20n%20divisors%20that%20are%20also%20Lucas%20numbers/prog.sf)
        * [Smallest number k such that sigma(sigma(k)) >= n*k](./oeis-research/Michel%20Marcus/Smallest%20number%20k%20such%20that%20sigma(sigma(k))%20>=%20n*k)
            * [search.pl](./oeis-research/Michel%20Marcus/Smallest%20number%20k%20such%20that%20sigma(sigma(k))%20>=%20n*k/search.pl)
            * [smooth.pl](./oeis-research/Michel%20Marcus/Smallest%20number%20k%20such%20that%20sigma(sigma(k))%20>=%20n*k/smooth.pl)
        * [Sum of first k divisors equal j+1 for non-squares of primes](./oeis-research/Michel%20Marcus/Sum%20of%20first%20k%20divisors%20equal%20j+1%20for%20non-squares%20of%20primes)
            * [faster.pl](./oeis-research/Michel%20Marcus/Sum%20of%20first%20k%20divisors%20equal%20j+1%20for%20non-squares%20of%20primes/faster.pl)
            * [smooth numbers generalized.pl](./oeis-research/Michel%20Marcus/Sum%20of%20first%20k%20divisors%20equal%20j+1%20for%20non-squares%20of%20primes/smooth_numbers_generalized.pl)
            * [x.pl](./oeis-research/Michel%20Marcus/Sum%20of%20first%20k%20divisors%20equal%20j+1%20for%20non-squares%20of%20primes/x.pl)
    * [Miles Englezou](./oeis-research/Miles%20Englezou)
        * [Least k such that k + A005117(i) is squarefree with i prime factors, for 1 <= i <= n](./oeis-research/Miles%20Englezou/Least%20k%20such%20that%20k%20+%20A005117(i)%20is%20squarefree%20with%20i%20prime%20factors,%20for%201%20<=%20i%20<=%20n)
            * [prog.pl](./oeis-research/Miles%20Englezou/Least%20k%20such%20that%20k%20+%20A005117(i)%20is%20squarefree%20with%20i%20prime%20factors,%20for%201%20<=%20i%20<=%20n/prog.pl)
    * [Mohammed Bouayoun](./oeis-research/Mohammed%20Bouayoun)
        * [Numbers k such that A061015(k) is prime](./oeis-research/Mohammed%20Bouayoun/Numbers%20k%20such%20that%20A061015(k)%20is%20prime)
            * [prog.sf](./oeis-research/Mohammed%20Bouayoun/Numbers%20k%20such%20that%20A061015(k)%20is%20prime/prog.sf)
    * [Muniru A Asiru](./oeis-research/Muniru%20A%20Asiru)
        * [Primes of the form 5^k + 2*k](./oeis-research/Muniru%20A%20Asiru/Primes%20of%20the%20form%205^k%20+%202*k)
            * [prog.pl](./oeis-research/Muniru%20A%20Asiru/Primes%20of%20the%20form%205^k%20+%202*k/prog.pl)
    * [N. J. A. Sloane](./oeis-research/N.%20J.%20A.%20Sloane)
        * [A(1)=3, b(n) = Product {k=1..n} a(k), a(n+1) is the largest prime factor of (b(n)-1)](./oeis-research/N.%20J.%20A.%20Sloane/a(1)=3,%20b(n)%20=%20Product_{k=1..n}%20a(k),%20a(n+1)%20is%20the%20largest%20prime%20factor%20of%20(b(n)-1))
            * [prog.sf](./oeis-research/N.%20J.%20A.%20Sloane/a(1)=3,%20b(n)%20=%20Product_{k=1..n}%20a(k),%20a(n+1)%20is%20the%20largest%20prime%20factor%20of%20(b(n)-1)/prog.sf)
        * [A(n) = largest prime factor of the number with decimal expansion 20305070...0p n where p n = n-th prime](./oeis-research/N.%20J.%20A.%20Sloane/a(n)%20=%20largest%20prime%20factor%20of%20the%20number%20with%20decimal%20expansion%2020305070...0p_n%20where%20p_n%20=%20n-th%20prime)
            * [prog.sf](./oeis-research/N.%20J.%20A.%20Sloane/a(n)%20=%20largest%20prime%20factor%20of%20the%20number%20with%20decimal%20expansion%2020305070...0p_n%20where%20p_n%20=%20n-th%20prime/prog.sf)
        * [A(n) is the largest prime factor of 2^p - p^2 where p is the n-th prime](./oeis-research/N.%20J.%20A.%20Sloane/a(n)%20is%20the%20largest%20prime%20factor%20of%202^p%20-%20p^2%20where%20p%20is%20the%20n-th%20prime)
            * [prog.sf](./oeis-research/N.%20J.%20A.%20Sloane/a(n)%20is%20the%20largest%20prime%20factor%20of%202^p%20-%20p^2%20where%20p%20is%20the%20n-th%20prime/prog.sf)
        * [Carmichael numbers of special form](./oeis-research/N.%20J.%20A.%20Sloane/Carmichael%20numbers%20of%20special%20form)
            * [extend.pl](./oeis-research/N.%20J.%20A.%20Sloane/Carmichael%20numbers%20of%20special%20form/extend.pl)
            * [isok.sf](./oeis-research/N.%20J.%20A.%20Sloane/Carmichael%20numbers%20of%20special%20form/isok.sf)
        * [Euclid-Mullin sequence: a(1) = 2, a(n+1) is largest prime factor of Product {k=1..n} a(k) + 1](./oeis-research/N.%20J.%20A.%20Sloane/Euclid-Mullin%20sequence:%20a(1)%20=%202,%20a(n+1)%20is%20largest%20prime%20factor%20of%20Product_{k=1..n}%20a(k)%20+%201)
            * [prog.sf](./oeis-research/N.%20J.%20A.%20Sloane/Euclid-Mullin%20sequence:%20a(1)%20=%202,%20a(n+1)%20is%20largest%20prime%20factor%20of%20Product_{k=1..n}%20a(k)%20+%201/prog.sf)
        * [Largest prime factor of (p^p-1) over (p-1) where p = prime(n)](./oeis-research/N.%20J.%20A.%20Sloane/Largest%20prime%20factor%20of%20(p^p-1)%20over%20(p-1)%20where%20p%20=%20prime(n))
            * [prog.sf](./oeis-research/N.%20J.%20A.%20Sloane/Largest%20prime%20factor%20of%20(p^p-1)%20over%20(p-1)%20where%20p%20=%20prime(n)/prog.sf)
        * [Largest prime factor of concatenation of primes with zeros](./oeis-research/N.%20J.%20A.%20Sloane/Largest%20prime%20factor%20of%20concatenation%20of%20primes%20with%20zeros)
            * [prog.sf](./oeis-research/N.%20J.%20A.%20Sloane/Largest%20prime%20factor%20of%20concatenation%20of%20primes%20with%20zeros/prog.sf)
            * [verify.sf](./oeis-research/N.%20J.%20A.%20Sloane/Largest%20prime%20factor%20of%20concatenation%20of%20primes%20with%20zeros/verify.sf)
        * [Least Carmichael number with n prime factors, or 0 if no such number exists](./oeis-research/N.%20J.%20A.%20Sloane/Least%20Carmichael%20number%20with%20n%20prime%20factors,%20or%200%20if%20no%20such%20number%20exists)
            * [prog.sf](./oeis-research/N.%20J.%20A.%20Sloane/Least%20Carmichael%20number%20with%20n%20prime%20factors,%20or%200%20if%20no%20such%20number%20exists/prog.sf)
        * [Numbers n such that sigma(sigma(n)) = n*k](./oeis-research/N.%20J.%20A.%20Sloane/Numbers%20n%20such%20that%20sigma(sigma(n))%20=%20n*k)
            * [prog.sf](./oeis-research/N.%20J.%20A.%20Sloane/Numbers%20n%20such%20that%20sigma(sigma(n))%20=%20n*k/prog.sf)
        * [Records in A073053](./oeis-research/N.%20J.%20A.%20Sloane/Records%20in%20A073053)
            * [prog.pl](./oeis-research/N.%20J.%20A.%20Sloane/Records%20in%20A073053/prog.pl)
        * [Smallest divisor of the Motzkin number not already in the sequence](./oeis-research/N.%20J.%20A.%20Sloane/Smallest%20divisor%20of%20the%20Motzkin%20number%20not%20already%20in%20the%20sequence)
            * [prog.sf](./oeis-research/N.%20J.%20A.%20Sloane/Smallest%20divisor%20of%20the%20Motzkin%20number%20not%20already%20in%20the%20sequence/prog.sf)
        * [Solution to x = 3*tanh(x)](./oeis-research/N.%20J.%20A.%20Sloane/Solution%20to%20x%20=%203*tanh(x))
            * [cfrac.sf](./oeis-research/N.%20J.%20A.%20Sloane/Solution%20to%20x%20=%203*tanh(x)/cfrac.sf)
            * [decimal.pl](./oeis-research/N.%20J.%20A.%20Sloane/Solution%20to%20x%20=%203*tanh(x)/decimal.pl)
        * [Zeros of an alternating sum of Euler totients](./oeis-research/N.%20J.%20A.%20Sloane/Zeros%20of%20an%20alternating%20sum%20of%20Euler%20totients)
            * [prog.pl](./oeis-research/N.%20J.%20A.%20Sloane/Zeros%20of%20an%20alternating%20sum%20of%20Euler%20totients/prog.pl)
        * [Zeros of an alternating sum of primes sequence](./oeis-research/N.%20J.%20A.%20Sloane/Zeros%20of%20an%20alternating%20sum%20of%20primes%20sequence)
            * [prog.pl](./oeis-research/N.%20J.%20A.%20Sloane/Zeros%20of%20an%20alternating%20sum%20of%20primes%20sequence/prog.pl)
    * [Naohiro Nomoto](./oeis-research/Naohiro%20Nomoto)
        * [Smallest number m such that sigma(x)*x = m has n solutions](./oeis-research/Naohiro%20Nomoto/Smallest%20number%20m%20such%20that%20sigma(x)*x%20=%20m%20has%20n%20solutions)
            * [from perfect numbers.sf](./oeis-research/Naohiro%20Nomoto/Smallest%20number%20m%20such%20that%20sigma(x)*x%20=%20m%20has%20n%20solutions/from_perfect_numbers.sf)
            * [smooth generate.pl](./oeis-research/Naohiro%20Nomoto/Smallest%20number%20m%20such%20that%20sigma(x)*x%20=%20m%20has%20n%20solutions/smooth_generate.pl)
    * [Nicolas Bělohoubek](./oeis-research/Nicolas%20Bělohoubek)
        * [A(n) is the smallest number > 1 that is not divisible by 10 but is divisible by the n-th power of the sum of its digits](./oeis-research/Nicolas%20Bělohoubek/a(n)%20is%20the%20smallest%20number%20>%201%20that%20is%20not%20divisible%20by%2010%20but%20is%20divisible%20by%20the%20n-th%20power%20of%20the%20sum%20of%20its%20digits)
            * [upper bounds.sf](./oeis-research/Nicolas%20Bělohoubek/a(n)%20is%20the%20smallest%20number%20>%201%20that%20is%20not%20divisible%20by%2010%20but%20is%20divisible%20by%20the%20n-th%20power%20of%20the%20sum%20of%20its%20digits/upper_bounds.sf)
    * [Nishant R. Gautam](./oeis-research/Nishant%20R.%20Gautam)
        * [Smallest integer k such that the iterated multiplicative-order chain k -> ord k(2) -> ord {ord k(2)}(2) -> ... reaches an even number in exactly n steps](./oeis-research/Nishant%20R.%20Gautam/Smallest%20integer%20k%20such%20that%20the%20iterated%20multiplicative-order%20chain%20k%20->%20ord_k(2)%20->%20ord_{ord_k(2)}(2)%20->%20...%20reaches%20an%20even%20number%20in%20exactly%20n%20steps)
            * [prog.pl](./oeis-research/Nishant%20R.%20Gautam/Smallest%20integer%20k%20such%20that%20the%20iterated%20multiplicative-order%20chain%20k%20->%20ord_k(2)%20->%20ord_{ord_k(2)}(2)%20->%20...%20reaches%20an%20even%20number%20in%20exactly%20n%20steps/prog.pl)
    * [Oliver Townsend](./oeis-research/Oliver%20Townsend)
        * [Integers k such that the fractional part of (3 over 2)^k gives a new record for the closest value to the fractional part of Pi](./oeis-research/Oliver%20Townsend/Integers%20k%20such%20that%20the%20fractional%20part%20of%20(3%20over%202)^k%20gives%20a%20new%20record%20for%20the%20closest%20value%20to%20the%20fractional%20part%20of%20Pi)
            * [prog.sf](./oeis-research/Oliver%20Townsend/Integers%20k%20such%20that%20the%20fractional%20part%20of%20(3%20over%202)^k%20gives%20a%20new%20record%20for%20the%20closest%20value%20to%20the%20fractional%20part%20of%20Pi/prog.sf)
    * [Olivier Gérard](./oeis-research/Olivier%20Gérard)
        * [Log of product of all primes between factorials](./oeis-research/Olivier%20Gérard/Log%20of%20product%20of%20all%20primes%20between%20factorials)
            * [native.pl](./oeis-research/Olivier%20Gérard/Log%20of%20product%20of%20all%20primes%20between%20factorials/native.pl)
            * [prog.pl](./oeis-research/Olivier%20Gérard/Log%20of%20product%20of%20all%20primes%20between%20factorials/prog.pl)
        * [Sum of primes between factorial](./oeis-research/Olivier%20Gérard/Sum%20of%20primes%20between%20factorial)
            * [prog.pl](./oeis-research/Olivier%20Gérard/Sum%20of%20primes%20between%20factorial/prog.pl)
    * [Omar E. Pol](./oeis-research/Omar%20E.%20Pol)
        * [Numbers n such that sigma(n) is a partition number](./oeis-research/Omar%20E.%20Pol/Numbers%20n%20such%20that%20sigma(n)%20is%20a%20partition%20number)
            * [prog.sf](./oeis-research/Omar%20E.%20Pol/Numbers%20n%20such%20that%20sigma(n)%20is%20a%20partition%20number/prog.sf)
    * [Ovidiu Bagdasar](./oeis-research/Ovidiu%20Bagdasar)
        * [Even composite integers m such that A006190(m)^2 == 1 (mod m)](./oeis-research/Ovidiu%20Bagdasar/Even%20composite%20integers%20m%20such%20that%20A006190(m)^2%20==%201%20(mod%20m))
            * [check.sf](./oeis-research/Ovidiu%20Bagdasar/Even%20composite%20integers%20m%20such%20that%20A006190(m)^2%20==%201%20(mod%20m)/check.sf)
            * [search.pl](./oeis-research/Ovidiu%20Bagdasar/Even%20composite%20integers%20m%20such%20that%20A006190(m)^2%20==%201%20(mod%20m)/search.pl)
    * [Paolo Galliani](./oeis-research/Paolo%20Galliani)
        * [Base16 primes](./oeis-research/Paolo%20Galliani/Base16%20primes)
            * [prog.pl](./oeis-research/Paolo%20Galliani/Base16%20primes/prog.pl)
        * [Reversed factorial is prime](./oeis-research/Paolo%20Galliani/Reversed%20factorial%20is%20prime)
            * [prog.sf](./oeis-research/Paolo%20Galliani/Reversed%20factorial%20is%20prime/prog.sf)
    * [Paolo P. Lava](./oeis-research/Paolo%20P.%20Lava)
        * [A(n) is the maximum prime factor of the concatenation of a(n-2) and a(n-1), with a(1)=1 and a(2)=2](./oeis-research/Paolo%20P.%20Lava/a(n)%20is%20the%20maximum%20prime%20factor%20of%20the%20concatenation%20of%20a(n-2)%20and%20a(n-1),%20with%20a(1)=1%20and%20a(2)=2)
            * [prog.sf](./oeis-research/Paolo%20P.%20Lava/a(n)%20is%20the%20maximum%20prime%20factor%20of%20the%20concatenation%20of%20a(n-2)%20and%20a(n-1),%20with%20a(1)=1%20and%20a(2)=2/prog.sf)
        * [A(n) is the maximum prime factor of the concatenation of all the previous terms, with a(1)=1, a(2)=2](./oeis-research/Paolo%20P.%20Lava/a(n)%20is%20the%20maximum%20prime%20factor%20of%20the%20concatenation%20of%20all%20the%20previous%20terms,%20with%20a(1)=1,%20a(2)=2)
            * [prog.sf](./oeis-research/Paolo%20P.%20Lava/a(n)%20is%20the%20maximum%20prime%20factor%20of%20the%20concatenation%20of%20all%20the%20previous%20terms,%20with%20a(1)=1,%20a(2)=2/prog.sf)
        * [Least number such that the concatenation of all the previous terms with it is squarefree and has n prime factors](./oeis-research/Paolo%20P.%20Lava/Least%20number%20such%20that%20the%20concatenation%20of%20all%20the%20previous%20terms%20with%20it%20is%20squarefree%20and%20has%20n%20prime%20factors)
            * [prog.sf](./oeis-research/Paolo%20P.%20Lava/Least%20number%20such%20that%20the%20concatenation%20of%20all%20the%20previous%20terms%20with%20it%20is%20squarefree%20and%20has%20n%20prime%20factors/prog.sf)
        * [Numbers k such that k divides sigma(k-2) + sigma(k-1) + sigma(k+1) + sigma(k+2)](./oeis-research/Paolo%20P.%20Lava/Numbers%20k%20such%20that%20k%20divides%20sigma(k-2)%20+%20sigma(k-1)%20+%20sigma(k+1)%20+%20sigma(k+2))
            * [prog.pl](./oeis-research/Paolo%20P.%20Lava/Numbers%20k%20such%20that%20k%20divides%20sigma(k-2)%20+%20sigma(k-1)%20+%20sigma(k+1)%20+%20sigma(k+2)/prog.pl)
        * [Quasi-narcissistic numbers: k-digit numbers n whose sum of k-th powers of their digits is equal to n +- 1](./oeis-research/Paolo%20P.%20Lava/Quasi-narcissistic%20numbers:%20k-digit%20numbers%20n%20whose%20sum%20of%20k-th%20powers%20of%20their%20digits%20is%20equal%20to%20n%20+-%201)
            * [prog.pl](./oeis-research/Paolo%20P.%20Lava/Quasi-narcissistic%20numbers:%20k-digit%20numbers%20n%20whose%20sum%20of%20k-th%20powers%20of%20their%20digits%20is%20equal%20to%20n%20+-%201/prog.pl)
            * [prog.sf](./oeis-research/Paolo%20P.%20Lava/Quasi-narcissistic%20numbers:%20k-digit%20numbers%20n%20whose%20sum%20of%20k-th%20powers%20of%20their%20digits%20is%20equal%20to%20n%20+-%201/prog.sf)
        * [Smallest composite number with n distinct prime factors with property that the concatenation of its distinct prime factors, in descending order, is a palindrome](./oeis-research/Paolo%20P.%20Lava/Smallest%20composite%20number%20with%20n%20distinct%20prime%20factors%20with%20property%20that%20the%20concatenation%20of%20its%20distinct%20prime%20factors,%20in%20descending%20order,%20is%20a%20palindrome)
            * [prog.sf](./oeis-research/Paolo%20P.%20Lava/Smallest%20composite%20number%20with%20n%20distinct%20prime%20factors%20with%20property%20that%20the%20concatenation%20of%20its%20distinct%20prime%20factors,%20in%20descending%20order,%20is%20a%20palindrome/prog.sf)
        * [Squarefree difference of semiprimes](./oeis-research/Paolo%20P.%20Lava/Squarefree%20difference%20of%20semiprimes)
            * [filter primes.sf](./oeis-research/Paolo%20P.%20Lava/Squarefree%20difference%20of%20semiprimes/filter_primes.sf)
            * [formula.sf](./oeis-research/Paolo%20P.%20Lava/Squarefree%20difference%20of%20semiprimes/formula.sf)
            * [generate.pl](./oeis-research/Paolo%20P.%20Lava/Squarefree%20difference%20of%20semiprimes/generate.pl)
            * [group trajectories.sf](./oeis-research/Paolo%20P.%20Lava/Squarefree%20difference%20of%20semiprimes/group_trajectories.sf)
            * [iterative upper-bounds.pl](./oeis-research/Paolo%20P.%20Lava/Squarefree%20difference%20of%20semiprimes/iterative_upper-bounds.pl)
            * [recursive upper-bounds.pl](./oeis-research/Paolo%20P.%20Lava/Squarefree%20difference%20of%20semiprimes/recursive_upper-bounds.pl)
            * [Squarefree semiprimes iteration.sf](./oeis-research/Paolo%20P.%20Lava/Squarefree%20difference%20of%20semiprimes/Squarefree%20semiprimes%20iteration.sf)
            * [trajectory.sf](./oeis-research/Paolo%20P.%20Lava/Squarefree%20difference%20of%20semiprimes/trajectory.sf)
            * [upper.pl](./oeis-research/Paolo%20P.%20Lava/Squarefree%20difference%20of%20semiprimes/upper.pl)
            * [upper bounds.sf](./oeis-research/Paolo%20P.%20Lava/Squarefree%20difference%20of%20semiprimes/upper_bounds.sf)
            * [verify.sf](./oeis-research/Paolo%20P.%20Lava/Squarefree%20difference%20of%20semiprimes/verify.sf)
    * [Paolo Xausa](./oeis-research/Paolo%20Xausa)
        * [Least number k such that omega(k) = n and the largest prime factor of k equals the sum of its remaining prime factors](./oeis-research/Paolo%20Xausa/Least%20number%20k%20such%20that%20omega(k)%20=%20n%20and%20the%20largest%20prime%20factor%20of%20k%20equals%20the%20sum%20of%20its%20remaining%20prime%20factors)
            * [generate.pl](./oeis-research/Paolo%20Xausa/Least%20number%20k%20such%20that%20omega(k)%20=%20n%20and%20the%20largest%20prime%20factor%20of%20k%20equals%20the%20sum%20of%20its%20remaining%20prime%20factors/generate.pl)
        * [Prime(n) nested prime(n) times](./oeis-research/Paolo%20Xausa/Prime(n)%20nested%20prime(n)%20times)
            * [prog.sf](./oeis-research/Paolo%20Xausa/Prime(n)%20nested%20prime(n)%20times/prog.sf)
    * [Patrick De Geest](./oeis-research/Patrick%20De%20Geest)
        * [A(n)-th prime has exactly n zeros](./oeis-research/Patrick%20De%20Geest/a(n)-th%20prime%20has%20exactly%20n%20zeros)
            * [prog.sf](./oeis-research/Patrick%20De%20Geest/a(n)-th%20prime%20has%20exactly%20n%20zeros/prog.sf)
        * [Index of smallest repunit having exactly n prime factors (counted with multiplicity)](./oeis-research/Patrick%20De%20Geest/Index%20of%20smallest%20repunit%20having%20exactly%20n%20prime%20factors%20(counted%20with%20multiplicity))
            * [prog.sf](./oeis-research/Patrick%20De%20Geest/Index%20of%20smallest%20repunit%20having%20exactly%20n%20prime%20factors%20(counted%20with%20multiplicity)/prog.sf)
            * [simple prog.sf](./oeis-research/Patrick%20De%20Geest/Index%20of%20smallest%20repunit%20having%20exactly%20n%20prime%20factors%20(counted%20with%20multiplicity)/simple_prog.sf)
        * [Palindromes of form n^2 + (n+1)^2](./oeis-research/Patrick%20De%20Geest/Palindromes%20of%20form%20n^2%20+%20(n+1)^2)
            * [prog.pl](./oeis-research/Patrick%20De%20Geest/Palindromes%20of%20form%20n^2%20+%20(n+1)^2/prog.pl)
        * [Smallest composite number with n distinct prime factors with property that the concatenation of its distinct prime factors is a palindrome](./oeis-research/Patrick%20De%20Geest/Smallest%20composite%20number%20with%20n%20distinct%20prime%20factors%20with%20property%20that%20the%20concatenation%20of%20its%20distinct%20prime%20factors%20is%20a%20palindrome)
            * [prog.sf](./oeis-research/Patrick%20De%20Geest/Smallest%20composite%20number%20with%20n%20distinct%20prime%20factors%20with%20property%20that%20the%20concatenation%20of%20its%20distinct%20prime%20factors%20is%20a%20palindrome/prog.sf)
        * [Smallest fraction using palindromes that approximates Pi](./oeis-research/Patrick%20De%20Geest/Smallest%20fraction%20using%20palindromes%20that%20approximates%20Pi)
            * [prog.sf](./oeis-research/Patrick%20De%20Geest/Smallest%20fraction%20using%20palindromes%20that%20approximates%20Pi/prog.sf)
        * [Smallest palindrome with exactly n palindromic prime factors (counted with multiplicity), and no other prime factors](./oeis-research/Patrick%20De%20Geest/Smallest%20palindrome%20with%20exactly%20n%20palindromic%20prime%20factors%20(counted%20with%20multiplicity),%20and%20no%20other%20prime%20factors)
            * [prog.sf](./oeis-research/Patrick%20De%20Geest/Smallest%20palindrome%20with%20exactly%20n%20palindromic%20prime%20factors%20(counted%20with%20multiplicity),%20and%20no%20other%20prime%20factors/prog.sf)
        * [Smallest squarefree palindrome with exactly n distinct prime factors](./oeis-research/Patrick%20De%20Geest/Smallest%20squarefree%20palindrome%20with%20exactly%20n%20distinct%20prime%20factors)
            * [prog.sf](./oeis-research/Patrick%20De%20Geest/Smallest%20squarefree%20palindrome%20with%20exactly%20n%20distinct%20prime%20factors/prog.sf)
            * [squarefree omega palindromes.jl](./oeis-research/Patrick%20De%20Geest/Smallest%20squarefree%20palindrome%20with%20exactly%20n%20distinct%20prime%20factors/squarefree_omega_palindromes.jl)
            * [squarefree omega palindromes.pl](./oeis-research/Patrick%20De%20Geest/Smallest%20squarefree%20palindrome%20with%20exactly%20n%20distinct%20prime%20factors/squarefree_omega_palindromes.pl)
            * [squarefree omega palindromes.py](./oeis-research/Patrick%20De%20Geest/Smallest%20squarefree%20palindrome%20with%20exactly%20n%20distinct%20prime%20factors/squarefree_omega_palindromes.py)
    * [Paul Vanderveen](./oeis-research/Paul%20Vanderveen)
        * [Smallest prime p == 3 (mod 4) such that all of 2,3,5,...,prime(n) are primitive roots mod p](./oeis-research/Paul%20Vanderveen/Smallest%20prime%20p%20==%203%20(mod%204)%20such%20that%20all%20of%202,3,5,...,prime(n)%20are%20primitive%20roots%20mod%20p)
            * [search.pl](./oeis-research/Paul%20Vanderveen/Smallest%20prime%20p%20==%203%20(mod%204)%20such%20that%20all%20of%202,3,5,...,prime(n)%20are%20primitive%20roots%20mod%20p/search.pl)
    * [Peter Kagey](./oeis-research/Peter%20Kagey)
        * [Least k such that A296062(k) = n](./oeis-research/Peter%20Kagey/Least%20k%20such%20that%20A296062(k)%20=%20n)
            * [prog.cpp](./oeis-research/Peter%20Kagey/Least%20k%20such%20that%20A296062(k)%20=%20n/prog.cpp)
    * [Peter Luschny](./oeis-research/Peter%20Luschny)
        * [Squarefree sequence conjecture](./oeis-research/Peter%20Luschny/Squarefree%20sequence%20conjecture)
            * [r.sf](./oeis-research/Peter%20Luschny/Squarefree%20sequence%20conjecture/r.sf)
    * [Petros Hadjicostas](./oeis-research/Petros%20Hadjicostas)
        * [Number of m X n arrays with rows being permutations](./oeis-research/Petros%20Hadjicostas/Number%20of%20m%20X%20n%20arrays%20with%20rows%20being%20permutations)
            * [formula.sf](./oeis-research/Petros%20Hadjicostas/Number%20of%20m%20X%20n%20arrays%20with%20rows%20being%20permutations/formula.sf)
    * [Philip Mizzi](./oeis-research/Philip%20Mizzi)
        * [Numbers k such that the sums of the first k and k+2 primes are also prime](./oeis-research/Philip%20Mizzi/Numbers%20k%20such%20that%20the%20sums%20of%20the%20first%20k%20and%20k+2%20primes%20are%20also%20prime)
            * [prog.pl](./oeis-research/Philip%20Mizzi/Numbers%20k%20such%20that%20the%20sums%20of%20the%20first%20k%20and%20k+2%20primes%20are%20also%20prime/prog.pl)
        * [Quadratic discriminants from consecutive palindromic primes](./oeis-research/Philip%20Mizzi/Quadratic%20discriminants%20from%20consecutive%20palindromic%20primes)
            * [prog.pl](./oeis-research/Philip%20Mizzi/Quadratic%20discriminants%20from%20consecutive%20palindromic%20primes/prog.pl)
    * [Pierre CAMI](./oeis-research/Pierre%20CAMI)
        * [Least k such that k * M(n) * M(n+1) + 1 is prime where M(n) = A000668(n)](./oeis-research/Pierre%20CAMI/Least%20k%20such%20that%20k%20*%20M(n)%20*%20M(n+1)%20+%201%20is%20prime%20where%20M(n)%20=%20A000668(n))
            * [prog.sf](./oeis-research/Pierre%20CAMI/Least%20k%20such%20that%20k%20*%20M(n)%20*%20M(n+1)%20+%201%20is%20prime%20where%20M(n)%20=%20A000668(n)/prog.sf)
        * [Least k such that prime(k)*2^(10^n) -1 is prime](./oeis-research/Pierre%20CAMI/Least%20k%20such%20that%20prime(k)*2^(10^n)%20-1%20is%20prime)
            * [prog.sf](./oeis-research/Pierre%20CAMI/Least%20k%20such%20that%20prime(k)*2^(10^n)%20-1%20is%20prime/prog.sf)
        * [Least prime p such that p^(2*prime(n))-p^prime(n)-1 is prime](./oeis-research/Pierre%20CAMI/Least%20prime%20p%20such%20that%20p^(2*prime(n))-p^prime(n)-1%20is%20prime)
            * [prog.sf](./oeis-research/Pierre%20CAMI/Least%20prime%20p%20such%20that%20p^(2*prime(n))-p^prime(n)-1%20is%20prime/prog.sf)
    * [Pontus von Brömssen](./oeis-research/Pontus%20von%20Brömssen)
        * [Numbers k such that the partition number p(k) = A000041(k) is a term of A057109](./oeis-research/Pontus%20von%20Brömssen/Numbers%20k%20such%20that%20the%20partition%20number%20p(k)%20=%20A000041(k)%20is%20a%20term%20of%20A057109)
            * [from factorizations.sf](./oeis-research/Pontus%20von%20Brömssen/Numbers%20k%20such%20that%20the%20partition%20number%20p(k)%20=%20A000041(k)%20is%20a%20term%20of%20A057109/from_factorizations.sf)
            * [prog.sf](./oeis-research/Pontus%20von%20Brömssen/Numbers%20k%20such%20that%20the%20partition%20number%20p(k)%20=%20A000041(k)%20is%20a%20term%20of%20A057109/prog.sf)
    * [Ralf Stephan](./oeis-research/Ralf%20Stephan)
        * [2^A101925(n)](./oeis-research/Ralf%20Stephan/2^A101925(n))
            * [formula.sf](./oeis-research/Ralf%20Stephan/2^A101925(n)/formula.sf)
    * [Reinhard Zumkeller](./oeis-research/Reinhard%20Zumkeller)
        * [Smallest m such that the n-th odd prime is the smallest number coprime to m and m+1](./oeis-research/Reinhard%20Zumkeller/Smallest%20m%20such%20that%20the%20n-th%20odd%20prime%20is%20the%20smallest%20number%20coprime%20to%20m%20and%20m+1)
            * [prog.sf](./oeis-research/Reinhard%20Zumkeller/Smallest%20m%20such%20that%20the%20n-th%20odd%20prime%20is%20the%20smallest%20number%20coprime%20to%20m%20and%20m+1/prog.sf)
        * [Smallest prime p such that 2*p+1 has n prime factors (with multiplicity)](./oeis-research/Reinhard%20Zumkeller/Smallest%20prime%20p%20such%20that%202*p+1%20has%20n%20prime%20factors%20(with%20multiplicity))
            * [prog.sf](./oeis-research/Reinhard%20Zumkeller/Smallest%20prime%20p%20such%20that%202*p+1%20has%20n%20prime%20factors%20(with%20multiplicity)/prog.sf)
    * [Richard N. Smith](./oeis-research/Richard%20N.%20Smith)
        * [Smallest prime factor of 2^(2^prime(n) - 1) - 1](./oeis-research/Richard%20N.%20Smith/Smallest%20prime%20factor%20of%202^(2^prime(n)%20-%201)%20-%201)
            * [prog.sf](./oeis-research/Richard%20N.%20Smith/Smallest%20prime%20factor%20of%202^(2^prime(n)%20-%201)%20-%201/prog.sf)
            * [search.pl](./oeis-research/Richard%20N.%20Smith/Smallest%20prime%20factor%20of%202^(2^prime(n)%20-%201)%20-%201/search.pl)
    * [Richard Pinch](./oeis-research/Richard%20Pinch)
        * [Smallest pseudoprime to base 2 with n prime factors](./oeis-research/Richard%20Pinch/Smallest%20pseudoprime%20to%20base%202%20with%20n%20prime%20factors)
            * [prog.pl](./oeis-research/Richard%20Pinch/Smallest%20pseudoprime%20to%20base%202%20with%20n%20prime%20factors/prog.pl)
            * [prog.sf](./oeis-research/Richard%20Pinch/Smallest%20pseudoprime%20to%20base%202%20with%20n%20prime%20factors/prog.sf)
            * [prog squarefree.pl](./oeis-research/Richard%20Pinch/Smallest%20pseudoprime%20to%20base%202%20with%20n%20prime%20factors/prog_squarefree.pl)
    * [Rick L. Shepherd](./oeis-research/Rick%20L.%20Shepherd)
        * [Largest prime factor of 10^(6*n) + 1](./oeis-research/Rick%20L.%20Shepherd/Largest%20prime%20factor%20of%2010^(6*n)%20+%201)
            * [prog.sf](./oeis-research/Rick%20L.%20Shepherd/Largest%20prime%20factor%20of%2010^(6*n)%20+%201/prog.sf)
        * [Smallest squarefree triangular number with exactly n prime factors](./oeis-research/Rick%20L.%20Shepherd/Smallest%20squarefree%20triangular%20number%20with%20exactly%20n%20prime%20factors)
            * [prog.sf](./oeis-research/Rick%20L.%20Shepherd/Smallest%20squarefree%20triangular%20number%20with%20exactly%20n%20prime%20factors/prog.sf)
    * [Robert FERREOL](./oeis-research/Robert%20FERREOL)
        * [Composite numbers k that divide A001644(k) - 1](./oeis-research/Robert%20FERREOL/Composite%20numbers%20k%20that%20divide%20A001644(k)%20-%201)
            * [prog.sf](./oeis-research/Robert%20FERREOL/Composite%20numbers%20k%20that%20divide%20A001644(k)%20-%201/prog.sf)
        * [Smallest prime factor of the n-th term in Sylvester's sequence](./oeis-research/Robert%20FERREOL/Smallest%20prime%20factor%20of%20the%20n-th%20term%20in%20Sylvester's%20sequence)
            * [prog.sf](./oeis-research/Robert%20FERREOL/Smallest%20prime%20factor%20of%20the%20n-th%20term%20in%20Sylvester's%20sequence/prog.sf)
    * [Robert G. Wilson v](./oeis-research/Robert%20G.%20Wilson%20v)
        * [A(n) is obtained by applying the map k -> prime(k) n times, starting at n](./oeis-research/Robert%20G.%20Wilson%20v/a(n)%20is%20obtained%20by%20applying%20the%20map%20k%20->%20prime(k)%20n%20times,%20starting%20at%20n)
            * [prog.sf](./oeis-research/Robert%20G.%20Wilson%20v/a(n)%20is%20obtained%20by%20applying%20the%20map%20k%20->%20prime(k)%20n%20times,%20starting%20at%20n/prog.sf)
        * [Index of first occurence of n in splitting function](./oeis-research/Robert%20G.%20Wilson%20v/Index%20of%20first%20occurence%20of%20n%20in%20splitting%20function)
            * [prog.pl](./oeis-research/Robert%20G.%20Wilson%20v/Index%20of%20first%20occurence%20of%20n%20in%20splitting%20function/prog.pl)
        * [Index of first occurence of n in splitting function -- upper-bounds](./oeis-research/Robert%20G.%20Wilson%20v/Index%20of%20first%20occurence%20of%20n%20in%20splitting%20function%20--%20upper-bounds)
            * [iterative difference of central divisors to reach zero.pl](./oeis-research/Robert%20G.%20Wilson%20v/Index%20of%20first%20occurence%20of%20n%20in%20splitting%20function%20--%20upper-bounds/iterative_difference_of_central_divisors_to_reach_zero.pl)
            * [t.pl](./oeis-research/Robert%20G.%20Wilson%20v/Index%20of%20first%20occurence%20of%20n%20in%20splitting%20function%20--%20upper-bounds/t.pl)
        * [Least semiprime for which n-1 iterations of "Look & Say" (A045918) all yield semiprimes, but not the n-th iteration](./oeis-research/Robert%20G.%20Wilson%20v/Least%20semiprime%20for%20which%20n-1%20iterations%20of%20"Look%20&%20Say"%20(A045918)%20all%20yield%20semiprimes,%20but%20not%20the%20n-th%20iteration)
            * [prog.pl](./oeis-research/Robert%20G.%20Wilson%20v/Least%20semiprime%20for%20which%20n-1%20iterations%20of%20"Look%20&%20Say"%20(A045918)%20all%20yield%20semiprimes,%20but%20not%20the%20n-th%20iteration/prog.pl)
        * [Number of 13-smooth numbers <= 10^n](./oeis-research/Robert%20G.%20Wilson%20v/Number%20of%2013-smooth%20numbers%20<=%2010^n)
            * [fast prog.sf](./oeis-research/Robert%20G.%20Wilson%20v/Number%20of%2013-smooth%20numbers%20<=%2010^n/fast_prog.sf)
            * [prog.pl](./oeis-research/Robert%20G.%20Wilson%20v/Number%20of%2013-smooth%20numbers%20<=%2010^n/prog.pl)
        * [Number of positive integers <= 10^n that are divisible by no prime exceeding p](./oeis-research/Robert%20G.%20Wilson%20v/Number%20of%20positive%20integers%20<=%2010^n%20that%20are%20divisible%20by%20no%20prime%20exceeding%20p)
            * [prog.sf](./oeis-research/Robert%20G.%20Wilson%20v/Number%20of%20positive%20integers%20<=%2010^n%20that%20are%20divisible%20by%20no%20prime%20exceeding%20p/prog.sf)
        * [Numbers k such that 8*factorial(k)-1 is prime](./oeis-research/Robert%20G.%20Wilson%20v/Numbers%20k%20such%20that%208*factorial(k)-1%20is%20prime)
            * [prog.sf](./oeis-research/Robert%20G.%20Wilson%20v/Numbers%20k%20such%20that%208*factorial(k)-1%20is%20prime/prog.sf)
        * [Smallest prime p such that bigomega(p+nextprime(p)) = n](./oeis-research/Robert%20G.%20Wilson%20v/Smallest%20prime%20p%20such%20that%20bigomega(p+nextprime(p))%20=%20n)
            * [generate.pl](./oeis-research/Robert%20G.%20Wilson%20v/Smallest%20prime%20p%20such%20that%20bigomega(p+nextprime(p))%20=%20n/generate.pl)
            * [prog.sf](./oeis-research/Robert%20G.%20Wilson%20v/Smallest%20prime%20p%20such%20that%20bigomega(p+nextprime(p))%20=%20n/prog.sf)
        * [The number of n-almost primes less than or equal to 10^n, starting with a(0)=1](./oeis-research/Robert%20G.%20Wilson%20v/The%20number%20of%20n-almost%20primes%20less%20than%20or%20equal%20to%2010^n,%20starting%20with%20a(0)=1)
            * [prog.sf](./oeis-research/Robert%20G.%20Wilson%20v/The%20number%20of%20n-almost%20primes%20less%20than%20or%20equal%20to%2010^n,%20starting%20with%20a(0)=1/prog.sf)
        * [The number of n-almost primes less than or equal to 12^n, starting with a(0)=1](./oeis-research/Robert%20G.%20Wilson%20v/The%20number%20of%20n-almost%20primes%20less%20than%20or%20equal%20to%2012^n,%20starting%20with%20a(0)=1)
            * [prog.sf](./oeis-research/Robert%20G.%20Wilson%20v/The%20number%20of%20n-almost%20primes%20less%20than%20or%20equal%20to%2012^n,%20starting%20with%20a(0)=1/prog.sf)
        * [The number of n-almost primes less than or equal to 8^n, starting with a(0)=1](./oeis-research/Robert%20G.%20Wilson%20v/The%20number%20of%20n-almost%20primes%20less%20than%20or%20equal%20to%208^n,%20starting%20with%20a(0)=1)
            * [prog.sf](./oeis-research/Robert%20G.%20Wilson%20v/The%20number%20of%20n-almost%20primes%20less%20than%20or%20equal%20to%208^n,%20starting%20with%20a(0)=1/prog.sf)
        * [The number of n-almost primes less than or equal to 9^n, starting with a(0)=1](./oeis-research/Robert%20G.%20Wilson%20v/The%20number%20of%20n-almost%20primes%20less%20than%20or%20equal%20to%209^n,%20starting%20with%20a(0)=1)
            * [prog.sf](./oeis-research/Robert%20G.%20Wilson%20v/The%20number%20of%20n-almost%20primes%20less%20than%20or%20equal%20to%209^n,%20starting%20with%20a(0)=1/prog.sf)
        * [The smallest k such that k! + 1 has exactly n prime factors (with multiplicity)](./oeis-research/Robert%20G.%20Wilson%20v/The%20smallest%20k%20such%20that%20k!%20+%201%20has%20exactly%20n%20prime%20factors%20(with%20multiplicity))
            * [is almost prime.sf](./oeis-research/Robert%20G.%20Wilson%20v/The%20smallest%20k%20such%20that%20k!%20+%201%20has%20exactly%20n%20prime%20factors%20(with%20multiplicity)/is_almost_prime.sf)
            * [prog.sf](./oeis-research/Robert%20G.%20Wilson%20v/The%20smallest%20k%20such%20that%20k!%20+%201%20has%20exactly%20n%20prime%20factors%20(with%20multiplicity)/prog.sf)
    * [Robert Israel](./oeis-research/Robert%20Israel)
        * [A(n) is the first prime p such that, if q is the next prime, (p*q+p+q) is 5^n times a prime](./oeis-research/Robert%20Israel/a(n)%20is%20the%20first%20prime%20p%20such%20that,%20if%20q%20is%20the%20next%20prime,%20(p*q+p+q)%20is%205^n%20times%20a%20prime)
            * [modular equation solutions.sf](./oeis-research/Robert%20Israel/a(n)%20is%20the%20first%20prime%20p%20such%20that,%20if%20q%20is%20the%20next%20prime,%20(p*q+p+q)%20is%205^n%20times%20a%20prime/modular_equation_solutions.sf)
        * [A(n) is the first prime that begins a sequence of exactly n consecutive primes that are emirps](./oeis-research/Robert%20Israel/a(n)%20is%20the%20first%20prime%20that%20begins%20a%20sequence%20of%20exactly%20n%20consecutive%20primes%20that%20are%20emirps)
            * [prog.pl](./oeis-research/Robert%20Israel/a(n)%20is%20the%20first%20prime%20that%20begins%20a%20sequence%20of%20exactly%20n%20consecutive%20primes%20that%20are%20emirps/prog.pl)
        * [A(n) is the least k such that k^j+2 is prime for j = 1 to n but not n+1](./oeis-research/Robert%20Israel/a(n)%20is%20the%20least%20k%20such%20that%20k^j+2%20is%20prime%20for%20j%20=%201%20to%20n%20but%20not%20n+1)
            * [prog.pl](./oeis-research/Robert%20Israel/a(n)%20is%20the%20least%20k%20such%20that%20k^j+2%20is%20prime%20for%20j%20=%201%20to%20n%20but%20not%20n+1/prog.pl)
            * [upper-bounds.pl](./oeis-research/Robert%20Israel/a(n)%20is%20the%20least%20k%20such%20that%20k^j+2%20is%20prime%20for%20j%20=%201%20to%20n%20but%20not%20n+1/upper-bounds.pl)
        * [A(n) is the least number that has exactly n divisors with sum of digits n](./oeis-research/Robert%20Israel/a(n)%20is%20the%20least%20number%20that%20has%20exactly%20n%20divisors%20with%20sum%20of%20digits%20n)
            * [find n-th term.pl](./oeis-research/Robert%20Israel/a(n)%20is%20the%20least%20number%20that%20has%20exactly%20n%20divisors%20with%20sum%20of%20digits%20n/find_n-th_term.pl)
            * [prog.pl](./oeis-research/Robert%20Israel/a(n)%20is%20the%20least%20number%20that%20has%20exactly%20n%20divisors%20with%20sum%20of%20digits%20n/prog.pl)
            * [recursive upper-bounds.pl](./oeis-research/Robert%20Israel/a(n)%20is%20the%20least%20number%20that%20has%20exactly%20n%20divisors%20with%20sum%20of%20digits%20n/recursive_upper-bounds.pl)
            * [smooth upper-bounds.pl](./oeis-research/Robert%20Israel/a(n)%20is%20the%20least%20number%20that%20has%20exactly%20n%20divisors%20with%20sum%20of%20digits%20n/smooth_upper-bounds.pl)
        * [First k such that if x(1) = k and x(i+1) = A062028(x(i)), x(1) to x(n) are all semiprimes but x(n+1) is not](./oeis-research/Robert%20Israel/First%20k%20such%20that%20if%20x(1)%20=%20k%20and%20x(i+1)%20=%20A062028(x(i)),%20x(1)%20to%20x(n)%20are%20all%20semiprimes%20but%20x(n+1)%20is%20not)
            * [prog.pl](./oeis-research/Robert%20Israel/First%20k%20such%20that%20if%20x(1)%20=%20k%20and%20x(i+1)%20=%20A062028(x(i)),%20x(1)%20to%20x(n)%20are%20all%20semiprimes%20but%20x(n+1)%20is%20not/prog.pl)
            * [prog 2.pl](./oeis-research/Robert%20Israel/First%20k%20such%20that%20if%20x(1)%20=%20k%20and%20x(i+1)%20=%20A062028(x(i)),%20x(1)%20to%20x(n)%20are%20all%20semiprimes%20but%20x(n+1)%20is%20not/prog_2.pl)
        * [First number k such that k + a(i) has n prime factors, counted with multiplicity, for all i < n](./oeis-research/Robert%20Israel/First%20number%20k%20such%20that%20k%20+%20a(i)%20has%20n%20prime%20factors,%20counted%20with%20multiplicity,%20for%20all%20i%20<%20n)
            * [prog.pl](./oeis-research/Robert%20Israel/First%20number%20k%20such%20that%20k%20+%20a(i)%20has%20n%20prime%20factors,%20counted%20with%20multiplicity,%20for%20all%20i%20<%20n/prog.pl)
            * [upperbounds.pl](./oeis-research/Robert%20Israel/First%20number%20k%20such%20that%20k%20+%20a(i)%20has%20n%20prime%20factors,%20counted%20with%20multiplicity,%20for%20all%20i%20<%20n/upperbounds.pl)
        * [First number that is the sum of k successive semiprimes for 1 <= k <= n](./oeis-research/Robert%20Israel/First%20number%20that%20is%20the%20sum%20of%20k%20successive%20semiprimes%20for%201%20<=%20k%20<=%20n)
            * [prog.pl](./oeis-research/Robert%20Israel/First%20number%20that%20is%20the%20sum%20of%20k%20successive%20semiprimes%20for%201%20<=%20k%20<=%20n/prog.pl)
            * [prog memory friendly.pl](./oeis-research/Robert%20Israel/First%20number%20that%20is%20the%20sum%20of%20k%20successive%20semiprimes%20for%201%20<=%20k%20<=%20n/prog_memory_friendly.pl)
        * [First prime p such that p - 2 and p + 2 both have exactly n prime factors, counted with multiplicity](./oeis-research/Robert%20Israel/First%20prime%20p%20such%20that%20p%20-%202%20and%20p%20+%202%20both%20have%20exactly%20n%20prime%20factors,%20counted%20with%20multiplicity)
            * [generate.pl](./oeis-research/Robert%20Israel/First%20prime%20p%20such%20that%20p%20-%202%20and%20p%20+%202%20both%20have%20exactly%20n%20prime%20factors,%20counted%20with%20multiplicity/generate.pl)
        * [Indices k such that A002533(k) is prime](./oeis-research/Robert%20Israel/Indices%20k%20such%20that%20A002533(k)%20is%20prime)
            * [prog.sf](./oeis-research/Robert%20Israel/Indices%20k%20such%20that%20A002533(k)%20is%20prime/prog.sf)
        * [Least k > 1 such that all divisors of (k^n-1) over (k-1) are == 1 (mod n)](./oeis-research/Robert%20Israel/Least%20k%20>%201%20such%20that%20all%20divisors%20of%20(k^n-1)%20over%20(k-1)%20are%20==%201%20(mod%20n))
            * [lower-bounds.sf](./oeis-research/Robert%20Israel/Least%20k%20>%201%20such%20that%20all%20divisors%20of%20(k^n-1)%20over%20(k-1)%20are%20==%201%20(mod%20n)/lower-bounds.sf)
        * [Least k for which A237196(k) = n](./oeis-research/Robert%20Israel/Least%20k%20for%20which%20A237196(k)%20=%20n)
            * [prog.jl](./oeis-research/Robert%20Israel/Least%20k%20for%20which%20A237196(k)%20=%20n/prog.jl)
            * [prog.pl](./oeis-research/Robert%20Israel/Least%20k%20for%20which%20A237196(k)%20=%20n/prog.pl)
            * [prog.sf](./oeis-research/Robert%20Israel/Least%20k%20for%20which%20A237196(k)%20=%20n/prog.sf)
        * [Least k such that k - i! is a semiprime for all i from 1 to n](./oeis-research/Robert%20Israel/Least%20k%20such%20that%20k%20-%20i!%20is%20a%20semiprime%20for%20all%20i%20from%201%20to%20n)
            * [prog.pl](./oeis-research/Robert%20Israel/Least%20k%20such%20that%20k%20-%20i!%20is%20a%20semiprime%20for%20all%20i%20from%201%20to%20n/prog.pl)
            * [prog fast.pl](./oeis-research/Robert%20Israel/Least%20k%20such%20that%20k%20-%20i!%20is%20a%20semiprime%20for%20all%20i%20from%201%20to%20n/prog_fast.pl)
            * [prog faster.pl](./oeis-research/Robert%20Israel/Least%20k%20such%20that%20k%20-%20i!%20is%20a%20semiprime%20for%20all%20i%20from%201%20to%20n/prog_faster.pl)
        * [Least n-gonal number that is the product of n distinct primes, or 0 if there are none](./oeis-research/Robert%20Israel/Least%20n-gonal%20number%20that%20is%20the%20product%20of%20n%20distinct%20primes,%20or%200%20if%20there%20are%20none)
            * [generate.sf](./oeis-research/Robert%20Israel/Least%20n-gonal%20number%20that%20is%20the%20product%20of%20n%20distinct%20primes,%20or%200%20if%20there%20are%20none/generate.sf)
            * [prog.sf](./oeis-research/Robert%20Israel/Least%20n-gonal%20number%20that%20is%20the%20product%20of%20n%20distinct%20primes,%20or%200%20if%20there%20are%20none/prog.sf)
        * [Least number k such that both k and k +'s have n prime divisors, counted with multiplicity, where's is the sum of the decimal digits of k](./oeis-research/Robert%20Israel/Least%20number%20k%20such%20that%20both%20k%20and%20k%20+%20s%20have%20n%20prime%20divisors,%20counted%20with%20multiplicity,%20where%20s%20is%20the%20sum%20of%20the%20decimal%20digits%20of%20k)
            * [generate.pl](./oeis-research/Robert%20Israel/Least%20number%20k%20such%20that%20both%20k%20and%20k%20+%20s%20have%20n%20prime%20divisors,%20counted%20with%20multiplicity,%20where%20s%20is%20the%20sum%20of%20the%20decimal%20digits%20of%20k/generate.pl)
        * [Least number k such that both k and k -'s have n prime divisors, counted with multiplicity, where's is the sum of the decimal digits of k](./oeis-research/Robert%20Israel/Least%20number%20k%20such%20that%20both%20k%20and%20k%20-%20s%20have%20n%20prime%20divisors,%20counted%20with%20multiplicity,%20where%20s%20is%20the%20sum%20of%20the%20decimal%20digits%20of%20k)
            * [generate.pl](./oeis-research/Robert%20Israel/Least%20number%20k%20such%20that%20both%20k%20and%20k%20-%20s%20have%20n%20prime%20divisors,%20counted%20with%20multiplicity,%20where%20s%20is%20the%20sum%20of%20the%20decimal%20digits%20of%20k/generate.pl)
        * [Least number of the form p^2 + q^2 - 2 for primes p and q that is an odd prime times 2^n, or -1 if there is no such number](./oeis-research/Robert%20Israel/Least%20number%20of%20the%20form%20p^2%20+%20q^2%20-%202%20for%20primes%20p%20and%20q%20that%20is%20an%20odd%20prime%20times%202^n,%20or%20-1%20if%20there%20is%20no%20such%20number)
            * [prog.sf](./oeis-research/Robert%20Israel/Least%20number%20of%20the%20form%20p^2%20+%20q^2%20-%202%20for%20primes%20p%20and%20q%20that%20is%20an%20odd%20prime%20times%202^n,%20or%20-1%20if%20there%20is%20no%20such%20number/prog.sf)
            * [prog2.pl](./oeis-research/Robert%20Israel/Least%20number%20of%20the%20form%20p^2%20+%20q^2%20-%202%20for%20primes%20p%20and%20q%20that%20is%20an%20odd%20prime%20times%202^n,%20or%20-1%20if%20there%20is%20no%20such%20number/prog2.pl)
            * [term from upper-bound.pl](./oeis-research/Robert%20Israel/Least%20number%20of%20the%20form%20p^2%20+%20q^2%20-%202%20for%20primes%20p%20and%20q%20that%20is%20an%20odd%20prime%20times%202^n,%20or%20-1%20if%20there%20is%20no%20such%20number/term_from_upper-bound.pl)
            * [upper-bounds.pl](./oeis-research/Robert%20Israel/Least%20number%20of%20the%20form%20p^2%20+%20q^2%20-%202%20for%20primes%20p%20and%20q%20that%20is%20an%20odd%20prime%20times%202^n,%20or%20-1%20if%20there%20is%20no%20such%20number/upper-bounds.pl)
        * [Least number with exactly two distinct base-10 digits and exactly n distinct prime factors, or -1 if there is no such number](./oeis-research/Robert%20Israel/Least%20number%20with%20exactly%20two%20distinct%20base-10%20digits%20and%20exactly%20n%20distinct%20prime%20factors,%20or%20-1%20if%20there%20is%20no%20such%20number)
            * [prog.pl](./oeis-research/Robert%20Israel/Least%20number%20with%20exactly%20two%20distinct%20base-10%20digits%20and%20exactly%20n%20distinct%20prime%20factors,%20or%20-1%20if%20there%20is%20no%20such%20number/prog.pl)
            * [prog.sf](./oeis-research/Robert%20Israel/Least%20number%20with%20exactly%20two%20distinct%20base-10%20digits%20and%20exactly%20n%20distinct%20prime%20factors,%20or%20-1%20if%20there%20is%20no%20such%20number/prog.sf)
            * [prog bigint.pl](./oeis-research/Robert%20Israel/Least%20number%20with%20exactly%20two%20distinct%20base-10%20digits%20and%20exactly%20n%20distinct%20prime%20factors,%20or%20-1%20if%20there%20is%20no%20such%20number/prog_bigint.pl)
        * [Least semiprime that is the first of n consecutive semiprimes s(1) ... s(n) such that s(i) - prime(i) are all equal](./oeis-research/Robert%20Israel/Least%20semiprime%20that%20is%20the%20first%20of%20n%20consecutive%20semiprimes%20s(1)%20...%20s(n)%20such%20that%20s(i)%20-%20prime(i)%20are%20all%20equal)
            * [prog.pl](./oeis-research/Robert%20Israel/Least%20semiprime%20that%20is%20the%20first%20of%20n%20consecutive%20semiprimes%20s(1)%20...%20s(n)%20such%20that%20s(i)%20-%20prime(i)%20are%20all%20equal/prog.pl)
        * [Numbers k such that 10^k + 3 is a semiprime](./oeis-research/Robert%20Israel/Numbers%20k%20such%20that%2010^k%20+%203%20is%20a%20semiprime)
            * [prog.sf](./oeis-research/Robert%20Israel/Numbers%20k%20such%20that%2010^k%20+%203%20is%20a%20semiprime/prog.sf)
        * [Numbers n such that binary(n) == 1 mod n](./oeis-research/Robert%20Israel/Numbers%20n%20such%20that%20binary(n)%20==%201%20mod%20n)
            * [prog.cpp](./oeis-research/Robert%20Israel/Numbers%20n%20such%20that%20binary(n)%20==%201%20mod%20n/prog.cpp)
            * [prog.pl](./oeis-research/Robert%20Israel/Numbers%20n%20such%20that%20binary(n)%20==%201%20mod%20n/prog.pl)
        * [Positions of records in A306440](./oeis-research/Robert%20Israel/Positions%20of%20records%20in%20A306440)
            * [prog.pl](./oeis-research/Robert%20Israel/Positions%20of%20records%20in%20A306440/prog.pl)
            * [smooth generator.pl](./oeis-research/Robert%20Israel/Positions%20of%20records%20in%20A306440/smooth_generator.pl)
            * [verify.sf](./oeis-research/Robert%20Israel/Positions%20of%20records%20in%20A306440/verify.sf)
        * [Primes p such that p^2 = (a+b+c)*b + 1 for some primitive Pythagorean triple (a,b,c)](./oeis-research/Robert%20Israel/Primes%20p%20such%20that%20p^2%20=%20(a+b+c)*b%20+%201%20for%20some%20primitive%20Pythagorean%20triple%20(a,b,c))
            * [prog.pl](./oeis-research/Robert%20Israel/Primes%20p%20such%20that%20p^2%20=%20(a+b+c)*b%20+%201%20for%20some%20primitive%20Pythagorean%20triple%20(a,b,c)/prog.pl)
        * [Primes prime(k) such that prime(k)^2 + prime(k+1)^2 - 1 is the square of a prime](./oeis-research/Robert%20Israel/Primes%20prime(k)%20such%20that%20prime(k)^2%20+%20prime(k+1)^2%20-%201%20is%20the%20square%20of%20a%20prime)
            * [prog.sf](./oeis-research/Robert%20Israel/Primes%20prime(k)%20such%20that%20prime(k)^2%20+%20prime(k+1)^2%20-%201%20is%20the%20square%20of%20a%20prime/prog.sf)
        * [Squares in A213544](./oeis-research/Robert%20Israel/Squares%20in%20A213544)
            * [prog.pl](./oeis-research/Robert%20Israel/Squares%20in%20A213544/prog.pl)
    * [Robert Price](./oeis-research/Robert%20Price)
        * [Numbers k such that (23^k - 2^k) over 21 is prime](./oeis-research/Robert%20Price/Numbers%20k%20such%20that%20(23^k%20-%202^k)%20over%2021%20is%20prime)
            * [prog.sf](./oeis-research/Robert%20Price/Numbers%20k%20such%20that%20(23^k%20-%202^k)%20over%2021%20is%20prime/prog.sf)
    * [Ryan Propper](./oeis-research/Ryan%20Propper)
        * [Least non-palindromic number k such that k and its digital reversal both have exactly n prime divisors](./oeis-research/Ryan%20Propper/Least%20non-palindromic%20number%20k%20such%20that%20k%20and%20its%20digital%20reversal%20both%20have%20exactly%20n%20prime%20divisors)
            * [prog.pl](./oeis-research/Ryan%20Propper/Least%20non-palindromic%20number%20k%20such%20that%20k%20and%20its%20digital%20reversal%20both%20have%20exactly%20n%20prime%20divisors/prog.pl)
            * [prog.sf](./oeis-research/Ryan%20Propper/Least%20non-palindromic%20number%20k%20such%20that%20k%20and%20its%20digital%20reversal%20both%20have%20exactly%20n%20prime%20divisors/prog.sf)
    * [Rémy Sigrist](./oeis-research/Rémy%20Sigrist)
        * [Smallest divisor of Fibonacci(n) not already in the sequence](./oeis-research/Rémy%20Sigrist/Smallest%20divisor%20of%20Fibonacci(n)%20not%20already%20in%20the%20sequence)
            * [prog.sf](./oeis-research/Rémy%20Sigrist/Smallest%20divisor%20of%20Fibonacci(n)%20not%20already%20in%20the%20sequence/prog.sf)
        * [Smallest divisor of the partition number not already in the sequence](./oeis-research/Rémy%20Sigrist/Smallest%20divisor%20of%20the%20partition%20number%20not%20already%20in%20the%20sequence)
            * [A307547.sf](./oeis-research/Rémy%20Sigrist/Smallest%20divisor%20of%20the%20partition%20number%20not%20already%20in%20the%20sequence/A307547.sf)
    * [Scott R. Shannon](./oeis-research/Scott%20R.%20Shannon)
        * [Composite numbers that divide the concatenation of the reverse of their ascending order prime factors, with repetition](./oeis-research/Scott%20R.%20Shannon/Composite%20numbers%20that%20divide%20the%20concatenation%20of%20the%20reverse%20of%20their%20ascending%20order%20prime%20factors,%20with%20repetition)
            * [prog.pl](./oeis-research/Scott%20R.%20Shannon/Composite%20numbers%20that%20divide%20the%20concatenation%20of%20the%20reverse%20of%20their%20ascending%20order%20prime%20factors,%20with%20repetition/prog.pl)
        * [Composite numbers that divide the concatenation of the reverse of their ascending order prime factors, with repetition, when written in binary](./oeis-research/Scott%20R.%20Shannon/Composite%20numbers%20that%20divide%20the%20concatenation%20of%20the%20reverse%20of%20their%20ascending%20order%20prime%20factors,%20with%20repetition,%20when%20written%20in%20binary)
            * [prog.pl](./oeis-research/Scott%20R.%20Shannon/Composite%20numbers%20that%20divide%20the%20concatenation%20of%20the%20reverse%20of%20their%20ascending%20order%20prime%20factors,%20with%20repetition,%20when%20written%20in%20binary/prog.pl)
        * [Composite numbers that divide the reverse of the concatenation of their ascending order prime factors, with repetition](./oeis-research/Scott%20R.%20Shannon/Composite%20numbers%20that%20divide%20the%20reverse%20of%20the%20concatenation%20of%20their%20ascending%20order%20prime%20factors,%20with%20repetition)
            * [prog.pl](./oeis-research/Scott%20R.%20Shannon/Composite%20numbers%20that%20divide%20the%20reverse%20of%20the%20concatenation%20of%20their%20ascending%20order%20prime%20factors,%20with%20repetition/prog.pl)
        * [Numbers that are a proper substring of the concatenation (with repetition) in decreasing order of their prime factors](./oeis-research/Scott%20R.%20Shannon/Numbers%20that%20are%20a%20proper%20substring%20of%20the%20concatenation%20(with%20repetition)%20in%20decreasing%20order%20of%20their%20prime%20factors)
            * [prog.pl](./oeis-research/Scott%20R.%20Shannon/Numbers%20that%20are%20a%20proper%20substring%20of%20the%20concatenation%20(with%20repetition)%20in%20decreasing%20order%20of%20their%20prime%20factors/prog.pl)
        * [Numbers that are a proper substring of the concatenation (with repetition) in increasing order of their prime factors](./oeis-research/Scott%20R.%20Shannon/Numbers%20that%20are%20a%20proper%20substring%20of%20the%20concatenation%20(with%20repetition)%20in%20increasing%20order%20of%20their%20prime%20factors)
            * [prog.pl](./oeis-research/Scott%20R.%20Shannon/Numbers%20that%20are%20a%20proper%20substring%20of%20the%20concatenation%20(with%20repetition)%20in%20increasing%20order%20of%20their%20prime%20factors/prog.pl)
        * [Smallest positive number that has yet appeared such that the sum of all terms a(1) + ... + a(n) has the same number of prime factors](./oeis-research/Scott%20R.%20Shannon/Smallest%20positive%20number%20that%20has%20yet%20appeared%20such%20that%20the%20sum%20of%20all%20terms%20a(1)%20+%20...%20+%20a(n)%20has%20the%20same%20number%20of%20prime%20factors)
            * [prog.sf](./oeis-research/Scott%20R.%20Shannon/Smallest%20positive%20number%20that%20has%20yet%20appeared%20such%20that%20the%20sum%20of%20all%20terms%20a(1)%20+%20...%20+%20a(n)%20has%20the%20same%20number%20of%20prime%20factors/prog.sf)
        * [The smallest composite number k that shares exactly n distinct prime factors with sopfr(k), the sum of the primes dividing k, with repetition](./oeis-research/Scott%20R.%20Shannon/The%20smallest%20composite%20number%20k%20that%20shares%20exactly%20n%20distinct%20prime%20factors%20with%20sopfr(k),%20the%20sum%20of%20the%20primes%20dividing%20k,%20with%20repetition)
            * [prog.pl](./oeis-research/Scott%20R.%20Shannon/The%20smallest%20composite%20number%20k%20that%20shares%20exactly%20n%20distinct%20prime%20factors%20with%20sopfr(k),%20the%20sum%20of%20the%20primes%20dividing%20k,%20with%20repetition/prog.pl)
            * [upper-bounds.pl](./oeis-research/Scott%20R.%20Shannon/The%20smallest%20composite%20number%20k%20that%20shares%20exactly%20n%20distinct%20prime%20factors%20with%20sopfr(k),%20the%20sum%20of%20the%20primes%20dividing%20k,%20with%20repetition/upper-bounds.pl)
        * [The smallest number whose prime factor concatenation, when written in base n, contains all digits 0,1,...,(n-1)](./oeis-research/Scott%20R.%20Shannon/The%20smallest%20number%20whose%20prime%20factor%20concatenation,%20when%20written%20in%20base%20n,%20contains%20all%20digits%200,1,...,(n-1))
            * [fast upper-bounds.sf](./oeis-research/Scott%20R.%20Shannon/The%20smallest%20number%20whose%20prime%20factor%20concatenation,%20when%20written%20in%20base%20n,%20contains%20all%20digits%200,1,...,(n-1)/fast_upper-bounds.sf)
            * [upper-bounds.pl](./oeis-research/Scott%20R.%20Shannon/The%20smallest%20number%20whose%20prime%20factor%20concatenation,%20when%20written%20in%20base%20n,%20contains%20all%20digits%200,1,...,(n-1)/upper-bounds.pl)
            * [upper-bounds.sf](./oeis-research/Scott%20R.%20Shannon/The%20smallest%20number%20whose%20prime%20factor%20concatenation,%20when%20written%20in%20base%20n,%20contains%20all%20digits%200,1,...,(n-1)/upper-bounds.sf)
    * [Seiichi Manyama](./oeis-research/Seiichi%20Manyama)
        * [Largest prime factor of 78557*2^n + 1](./oeis-research/Seiichi%20Manyama/Largest%20prime%20factor%20of%2078557*2^n%20+%201)
            * [prog.sf](./oeis-research/Seiichi%20Manyama/Largest%20prime%20factor%20of%2078557*2^n%20+%201/prog.sf)
        * [Largest prime factor of A020549(n) = (n!)^2 + 1](./oeis-research/Seiichi%20Manyama/Largest%20prime%20factor%20of%20A020549(n)%20=%20(n!)^2%20+%201)
            * [prog.sf](./oeis-research/Seiichi%20Manyama/Largest%20prime%20factor%20of%20A020549(n)%20=%20(n!)^2%20+%201/prog.sf)
        * [Least positive number k such that sigma(k) = n * sigma(k+1)](./oeis-research/Seiichi%20Manyama/Least%20positive%20number%20k%20such%20that%20sigma(k)%20=%20n%20*%20sigma(k+1))
            * [comb.pl](./oeis-research/Seiichi%20Manyama/Least%20positive%20number%20k%20such%20that%20sigma(k)%20=%20n%20*%20sigma(k+1)/comb.pl)
            * [smooth generate.pl](./oeis-research/Seiichi%20Manyama/Least%20positive%20number%20k%20such%20that%20sigma(k)%20=%20n%20*%20sigma(k+1)/smooth_generate.pl)
        * [Least positive number k such that sigma(k+1) = n * sigma(k)](./oeis-research/Seiichi%20Manyama/Least%20positive%20number%20k%20such%20that%20sigma(k+1)%20=%20n%20*%20sigma(k))
            * [smooth generate.pl](./oeis-research/Seiichi%20Manyama/Least%20positive%20number%20k%20such%20that%20sigma(k+1)%20=%20n%20*%20sigma(k)/smooth_generate.pl)
    * [Sergio Pimentel](./oeis-research/Sergio%20Pimentel)
        * [Abundant numbers](./oeis-research/Sergio%20Pimentel/Abundant%20numbers)
            * [abundant numbers generation.pl](./oeis-research/Sergio%20Pimentel/Abundant%20numbers/abundant_numbers_generation.pl)
    * [Sezai Ata](./oeis-research/Sezai%20Ata)
        * [Turkish numbers](./oeis-research/Sezai%20Ata/Turkish%20numbers)
            * [turkish numbers len.pl](./oeis-research/Sezai%20Ata/Turkish%20numbers/turkish_numbers_len.pl)
            * [turkish numbers len corrected.pl](./oeis-research/Sezai%20Ata/Turkish%20numbers/turkish_numbers_len_corrected.pl)
    * [Shyam Sunder Gupta](./oeis-research/Shyam%20Sunder%20Gupta)
        * [Carmichael numbers which are also base-2 strong pseudoprimes](./oeis-research/Shyam%20Sunder%20Gupta/Carmichael%20numbers%20which%20are%20also%20base-2%20strong%20pseudoprimes)
            * [prog.pl](./oeis-research/Shyam%20Sunder%20Gupta/Carmichael%20numbers%20which%20are%20also%20base-2%20strong%20pseudoprimes/prog.pl)
            * [prog faster.pl](./oeis-research/Shyam%20Sunder%20Gupta/Carmichael%20numbers%20which%20are%20also%20base-2%20strong%20pseudoprimes/prog_faster.pl)
        * [Index of smallest Fibonacci number with n prime factors when counted with multiplicity](./oeis-research/Shyam%20Sunder%20Gupta/Index%20of%20smallest%20Fibonacci%20number%20with%20n%20prime%20factors%20when%20counted%20with%20multiplicity)
            * [prog.sf](./oeis-research/Shyam%20Sunder%20Gupta/Index%20of%20smallest%20Fibonacci%20number%20with%20n%20prime%20factors%20when%20counted%20with%20multiplicity/prog.sf)
        * [Palindromic pseudoprimes to base 2](./oeis-research/Shyam%20Sunder%20Gupta/Palindromic%20pseudoprimes%20to%20base%202)
            * [generate pseudoprimes.pl](./oeis-research/Shyam%20Sunder%20Gupta/Palindromic%20pseudoprimes%20to%20base%202/generate_pseudoprimes.pl)
            * [palindromic generation.pl](./oeis-research/Shyam%20Sunder%20Gupta/Palindromic%20pseudoprimes%20to%20base%202/palindromic_generation.pl)
            * [smooth generation.pl](./oeis-research/Shyam%20Sunder%20Gupta/Palindromic%20pseudoprimes%20to%20base%202/smooth_generation.pl)
        * [Smallest titanic number with 3 distinct prime factors](./oeis-research/Shyam%20Sunder%20Gupta/Smallest%20titanic%20number%20with%203%20distinct%20prime%20factors)
            * [prog.sf](./oeis-research/Shyam%20Sunder%20Gupta/Smallest%20titanic%20number%20with%203%20distinct%20prime%20factors/prog.sf)
        * [Smallest triangular number with n prime factors (counted without multiplicity)](./oeis-research/Shyam%20Sunder%20Gupta/Smallest%20triangular%20number%20with%20n%20prime%20factors%20(counted%20without%20multiplicity))
            * [prog.sf](./oeis-research/Shyam%20Sunder%20Gupta/Smallest%20triangular%20number%20with%20n%20prime%20factors%20(counted%20without%20multiplicity)/prog.sf)
    * [Sidney Cadot](./oeis-research/Sidney%20Cadot)
        * [Number of odd semiprimes between 2^(n-1) and 2^n](./oeis-research/Sidney%20Cadot/Number%20of%20odd%20semiprimes%20between%202^(n-1)%20and%202^n)
            * [prog.sf](./oeis-research/Sidney%20Cadot/Number%20of%20odd%20semiprimes%20between%202^(n-1)%20and%202^n/prog.sf)
        * [Number of odd semiprimes less than 2^n](./oeis-research/Sidney%20Cadot/Number%20of%20odd%20semiprimes%20less%20than%202^n)
            * [prog.sf](./oeis-research/Sidney%20Cadot/Number%20of%20odd%20semiprimes%20less%20than%202^n/prog.sf)
    * [Sofia Lacerda](./oeis-research/Sofia%20Lacerda)
        * [Primes p such that gcd(ord p(2), ord p(3)) = 1](./oeis-research/Sofia%20Lacerda/Primes%20p%20such%20that%20gcd(ord_p(2),%20ord_p(3))%20=%201)
            * [search.pl](./oeis-research/Sofia%20Lacerda/Primes%20p%20such%20that%20gcd(ord_p(2),%20ord_p(3))%20=%201/search.pl)
    * [Stefano Spezia](./oeis-research/Stefano%20Spezia)
        * [A(n) is the n-digit positive number with no trailing zeros and coprime to its digital reversal R(a(n)) at which abs(a(n) over R(a(n))-Pi) is minimized](./oeis-research/Stefano%20Spezia/a(n)%20is%20the%20n-digit%20positive%20number%20with%20no%20trailing%20zeros%20and%20coprime%20to%20its%20digital%20reversal%20R(a(n))%20at%20which%20abs(a(n)%20over%20R(a(n))-Pi)%20is%20minimized)
            * [prog.pl](./oeis-research/Stefano%20Spezia/a(n)%20is%20the%20n-digit%20positive%20number%20with%20no%20trailing%20zeros%20and%20coprime%20to%20its%20digital%20reversal%20R(a(n))%20at%20which%20abs(a(n)%20over%20R(a(n))-Pi)%20is%20minimized/prog.pl)
        * [Number of positive integers with n digits that are the product of two integers ending with 3](./oeis-research/Stefano%20Spezia/Number%20of%20positive%20integers%20with%20n%20digits%20that%20are%20the%20product%20of%20two%20integers%20ending%20with%203)
            * [prog.pl](./oeis-research/Stefano%20Spezia/Number%20of%20positive%20integers%20with%20n%20digits%20that%20are%20the%20product%20of%20two%20integers%20ending%20with%203/prog.pl)
    * [T. D. Noe](./oeis-research/T.%20D.%20Noe)
        * [Least prime p such that 2x^2 + p produces primes for x=0..n-1 and composite for x=n](./oeis-research/T.%20D.%20Noe/Least%20prime%20p%20such%20that%202x^2%20+%20p%20produces%20primes%20for%20x=0..n-1%20and%20composite%20for%20x=n)
            * [sieve.pl](./oeis-research/T.%20D.%20Noe/Least%20prime%20p%20such%20that%202x^2%20+%20p%20produces%20primes%20for%20x=0..n-1%20and%20composite%20for%20x=n/sieve.pl)
        * [Least prime p such that p^2+1 is the product of n distinct primes](./oeis-research/T.%20D.%20Noe/Least%20prime%20p%20such%20that%20p^2+1%20is%20the%20product%20of%20n%20distinct%20primes)
            * [prog.pl](./oeis-research/T.%20D.%20Noe/Least%20prime%20p%20such%20that%20p^2+1%20is%20the%20product%20of%20n%20distinct%20primes/prog.pl)
            * [prog.sf](./oeis-research/T.%20D.%20Noe/Least%20prime%20p%20such%20that%20p^2+1%20is%20the%20product%20of%20n%20distinct%20primes/prog.sf)
        * [Least prime p such that x^2+x+p produces primes for x=0..n-1 and composite for x=n](./oeis-research/T.%20D.%20Noe/Least%20prime%20p%20such%20that%20x^2+x+p%20produces%20primes%20for%20x=0..n-1%20and%20composite%20for%20x=n)
            * [sieve.pl](./oeis-research/T.%20D.%20Noe/Least%20prime%20p%20such%20that%20x^2+x+p%20produces%20primes%20for%20x=0..n-1%20and%20composite%20for%20x=n/sieve.pl)
        * [Smallest odd primitive abundant number (A006038) having n distinct prime factors](./oeis-research/T.%20D.%20Noe/Smallest%20odd%20primitive%20abundant%20number%20(A006038)%20having%20n%20distinct%20prime%20factors)
            * [prog.sf](./oeis-research/T.%20D.%20Noe/Smallest%20odd%20primitive%20abundant%20number%20(A006038)%20having%20n%20distinct%20prime%20factors/prog.sf)
        * [Smallest odd primitive abundant number having n distinct prime factors](./oeis-research/T.%20D.%20Noe/Smallest%20odd%20primitive%20abundant%20number%20having%20n%20distinct%20prime%20factors)
            * [generate.pl](./oeis-research/T.%20D.%20Noe/Smallest%20odd%20primitive%20abundant%20number%20having%20n%20distinct%20prime%20factors/generate.pl)
            * [squarefree generate.pl](./oeis-research/T.%20D.%20Noe/Smallest%20odd%20primitive%20abundant%20number%20having%20n%20distinct%20prime%20factors/squarefree_generate.pl)
    * [Tejo Vrush](./oeis-research/Tejo%20Vrush)
        * [A(n) is the least k such that A348172(k) = n or 0 if no such k exists](./oeis-research/Tejo%20Vrush/a(n)%20is%20the%20least%20k%20such%20that%20A348172(k)%20=%20n%20or%200%20if%20no%20such%20k%20exists)
            * [smooth generate.pl](./oeis-research/Tejo%20Vrush/a(n)%20is%20the%20least%20k%20such%20that%20A348172(k)%20=%20n%20or%200%20if%20no%20such%20k%20exists/smooth_generate.pl)
            * [smooth generate quotient.pl](./oeis-research/Tejo%20Vrush/a(n)%20is%20the%20least%20k%20such%20that%20A348172(k)%20=%20n%20or%200%20if%20no%20such%20k%20exists/smooth_generate_quotient.pl)
        * [A(n) is the number of positive k (can be equal to n) such that A000005(n) over n = A000005(k) over k](./oeis-research/Tejo%20Vrush/a(n)%20is%20the%20number%20of%20positive%20k%20(can%20be%20equal%20to%20n)%20such%20that%20A000005(n)%20over%20n%20=%20A000005(k)%20over%20k)
            * [prog.pl](./oeis-research/Tejo%20Vrush/a(n)%20is%20the%20number%20of%20positive%20k%20(can%20be%20equal%20to%20n)%20such%20that%20A000005(n)%20over%20n%20=%20A000005(k)%20over%20k/prog.pl)
    * [Thomas Gajdek](./oeis-research/Thomas%20Gajdek)
        * [Numbers k such that 2^(k-1) - k is prime](./oeis-research/Thomas%20Gajdek/Numbers%20k%20such%20that%202^(k-1)%20-%20k%20is%20prime)
            * [prog.pl](./oeis-research/Thomas%20Gajdek/Numbers%20k%20such%20that%202^(k-1)%20-%20k%20is%20prime/prog.pl)
    * [Thomas Ordowski](./oeis-research/Thomas%20Ordowski)
        * [12 June](./oeis-research/Thomas%20Ordowski/12%20June)
            * [prog.pl](./oeis-research/Thomas%20Ordowski/12%20June/prog.pl)
        * [12 May](./oeis-research/Thomas%20Ordowski/12%20May)
            * [cexamples.sf](./oeis-research/Thomas%20Ordowski/12%20May/cexamples.sf)
            * [pseudoprime search.pl](./oeis-research/Thomas%20Ordowski/12%20May/pseudoprime_search.pl)
            * [test-pseudoprime search.pl](./oeis-research/Thomas%20Ordowski/12%20May/test-pseudoprime_search.pl)
        * [13 June](./oeis-research/Thomas%20Ordowski/13%20June)
            * [x.pl](./oeis-research/Thomas%20Ordowski/13%20June/x.pl)
        * [13 May](./oeis-research/Thomas%20Ordowski/13%20May)
            * [prorg.pl](./oeis-research/Thomas%20Ordowski/13%20May/prorg.pl)
            * [x.sf](./oeis-research/Thomas%20Ordowski/13%20May/x.sf)
        * [15 May](./oeis-research/Thomas%20Ordowski/15%20May)
            * [isok.sf](./oeis-research/Thomas%20Ordowski/15%20May/isok.sf)
            * [large chernick.pl](./oeis-research/Thomas%20Ordowski/15%20May/large_chernick.pl)
            * [solovay.pl](./oeis-research/Thomas%20Ordowski/15%20May/solovay.pl)
            * [test-pseudoprime search.pl](./oeis-research/Thomas%20Ordowski/15%20May/test-pseudoprime_search.pl)
            * [test-pseudoprime search 2.pl](./oeis-research/Thomas%20Ordowski/15%20May/test-pseudoprime_search_2.pl)
            * [upper-bounds with residue.pl](./oeis-research/Thomas%20Ordowski/15%20May/upper-bounds_with_residue.pl)
        * [17 May](./oeis-research/Thomas%20Ordowski/17%20May)
            * [lucas.sf](./oeis-research/Thomas%20Ordowski/17%20May/lucas.sf)
        * [18 May](./oeis-research/Thomas%20Ordowski/18%20May)
            * [u.sf](./oeis-research/Thomas%20Ordowski/18%20May/u.sf)
            * [x.pl](./oeis-research/Thomas%20Ordowski/18%20May/x.pl)
        * [2 July 2019](./oeis-research/Thomas%20Ordowski/2%20July%202019)
            * [wilson-gauss-trifactorial.sf](./oeis-research/Thomas%20Ordowski/2%20July%202019/wilson-gauss-trifactorial.sf)
        * [22 July - comments](./oeis-research/Thomas%20Ordowski/22%20July%20-%20comments)
            * [a.sf](./oeis-research/Thomas%20Ordowski/22%20July%20-%20comments/a.sf)
            * [b.sf](./oeis-research/Thomas%20Ordowski/22%20July%20-%20comments/b.sf)
        * [24 May](./oeis-research/Thomas%20Ordowski/24%20May)
            * [sidef prog.sf](./oeis-research/Thomas%20Ordowski/24%20May/sidef_prog.sf)
        * [9 June](./oeis-research/Thomas%20Ordowski/9%20June)
            * [test-pseudoprime search 2.pl](./oeis-research/Thomas%20Ordowski/9%20June/test-pseudoprime_search_2.pl)
        * [A(n) is the smallest b > 0 such that b^(2n) + 1 has all prime divisors p == 1 (mod 2n)](./oeis-research/Thomas%20Ordowski/a(n)%20is%20the%20smallest%20b%20>%200%20such%20that%20b^(2n)%20+%201%20has%20all%20prime%20divisors%20p%20==%201%20(mod%202n))
            * [lower-bounds.sf](./oeis-research/Thomas%20Ordowski/a(n)%20is%20the%20smallest%20b%20>%200%20such%20that%20b^(2n)%20+%201%20has%20all%20prime%20divisors%20p%20==%201%20(mod%202n)/lower-bounds.sf)
        * [A(n) is the smallest k with n prime factors such that p^k == p (mod k) for every prime p dividing k](./oeis-research/Thomas%20Ordowski/a(n)%20is%20the%20smallest%20k%20with%20n%20prime%20factors%20such%20that%20p^k%20==%20p%20(mod%20k)%20for%20every%20prime%20p%20dividing%20k)
            * [prog.pl](./oeis-research/Thomas%20Ordowski/a(n)%20is%20the%20smallest%20k%20with%20n%20prime%20factors%20such%20that%20p^k%20==%20p%20(mod%20k)%20for%20every%20prime%20p%20dividing%20k/prog.pl)
            * [prog.sf](./oeis-research/Thomas%20Ordowski/a(n)%20is%20the%20smallest%20k%20with%20n%20prime%20factors%20such%20that%20p^k%20==%20p%20(mod%20k)%20for%20every%20prime%20p%20dividing%20k/prog.sf)
        * [A(n) is the smallest number k with n prime factors such that p + div(k,p) is prime for every prime p | k](./oeis-research/Thomas%20Ordowski/a(n)%20is%20the%20smallest%20number%20k%20with%20n%20prime%20factors%20such%20that%20p%20+%20div(k,p)%20is%20prime%20for%20every%20prime%20p%20|%20k)
            * [prog.pl](./oeis-research/Thomas%20Ordowski/a(n)%20is%20the%20smallest%20number%20k%20with%20n%20prime%20factors%20such%20that%20p%20+%20div(k,p)%20is%20prime%20for%20every%20prime%20p%20|%20k/prog.pl)
            * [prog.sf](./oeis-research/Thomas%20Ordowski/a(n)%20is%20the%20smallest%20number%20k%20with%20n%20prime%20factors%20such%20that%20p%20+%20div(k,p)%20is%20prime%20for%20every%20prime%20p%20|%20k/prog.sf)
        * [A(n) is the smallest odd b > 1 such that (b^(2n) + 1) over 2 has all prime divisors p == 1 (mod 2n)](./oeis-research/Thomas%20Ordowski/a(n)%20is%20the%20smallest%20odd%20b%20>%201%20such%20that%20(b^(2n)%20+%201)%20over%202%20has%20all%20prime%20divisors%20p%20==%201%20(mod%202n))
            * [lower-bounds.sf](./oeis-research/Thomas%20Ordowski/a(n)%20is%20the%20smallest%20odd%20b%20>%201%20such%20that%20(b^(2n)%20+%201)%20over%202%20has%20all%20prime%20divisors%20p%20==%201%20(mod%202n)/lower-bounds.sf)
        * [Conjecture 13 July 2022](./oeis-research/Thomas%20Ordowski/Conjecture%2013%20July%202022)
            * [prog.sf](./oeis-research/Thomas%20Ordowski/Conjecture%2013%20July%202022/prog.sf)
        * [Divisibility of numerators of harmonic numbers](./oeis-research/Thomas%20Ordowski/Divisibility%20of%20numerators%20of%20harmonic%20numbers)
            * [harmonic numerator divisibility.sf](./oeis-research/Thomas%20Ordowski/Divisibility%20of%20numerators%20of%20harmonic%20numbers/harmonic_numerator_divisibility.sf)
        * [Factor 2n](./oeis-research/Thomas%20Ordowski/Factor%202n)
            * [x.pl](./oeis-research/Thomas%20Ordowski/Factor%202n/x.pl)
            * [z.pl](./oeis-research/Thomas%20Ordowski/Factor%202n/z.pl)
            * [z.sf](./oeis-research/Thomas%20Ordowski/Factor%202n/z.sf)
        * [Least k > 1 such that all divisors d of (k^(2n+1)+1) over (k+1) satisfy d == 1 (mod 2n+1)](./oeis-research/Thomas%20Ordowski/Least%20k%20>%201%20such%20that%20all%20divisors%20d%20of%20(k^(2n+1)+1)%20over%20(k+1)%20satisfy%20d%20==%201%20(mod%202n+1))
            * [lower-bounds.sf](./oeis-research/Thomas%20Ordowski/Least%20k%20>%201%20such%20that%20all%20divisors%20d%20of%20(k^(2n+1)+1)%20over%20(k+1)%20satisfy%20d%20==%201%20(mod%202n+1)/lower-bounds.sf)
        * [Non-residue pseudoprimes](./oeis-research/Thomas%20Ordowski/Non-residue%20pseudoprimes)
            * [non residue.sf](./oeis-research/Thomas%20Ordowski/Non-residue%20pseudoprimes/non_residue.sf)
            * [prog.pl](./oeis-research/Thomas%20Ordowski/Non-residue%20pseudoprimes/prog.pl)
            * [prog2.pl](./oeis-research/Thomas%20Ordowski/Non-residue%20pseudoprimes/prog2.pl)
            * [prog3 optimized.pl](./oeis-research/Thomas%20Ordowski/Non-residue%20pseudoprimes/prog3_optimized.pl)
            * [prog4 optimized.pl](./oeis-research/Thomas%20Ordowski/Non-residue%20pseudoprimes/prog4_optimized.pl)
            * [semiprimes search.pl](./oeis-research/Thomas%20Ordowski/Non-residue%20pseudoprimes/semiprimes_search.pl)
            * [upper-bounds.pl](./oeis-research/Thomas%20Ordowski/Non-residue%20pseudoprimes/upper-bounds.pl)
            * [upper-bounds multiple.pl](./oeis-research/Thomas%20Ordowski/Non-residue%20pseudoprimes/upper-bounds_multiple.pl)
            * [upper-bounds optimized.pl](./oeis-research/Thomas%20Ordowski/Non-residue%20pseudoprimes/upper-bounds_optimized.pl)
            * [upper-bounds with residue.pl](./oeis-research/Thomas%20Ordowski/Non-residue%20pseudoprimes/upper-bounds_with_residue.pl)
        * [Primes sum of squares](./oeis-research/Thomas%20Ordowski/Primes%20sum%20of%20squares)
            * [thomas primes sum of squares.pl](./oeis-research/Thomas%20Ordowski/Primes%20sum%20of%20squares/thomas_primes_sum_of_squares.pl)
        * [Smallest k such that 2^(2^n+1)-1 + 2^k is prime, or -1 if no such k exists](./oeis-research/Thomas%20Ordowski/Smallest%20k%20such%20that%202^(2^n+1)-1%20+%202^k%20is%20prime,%20or%20-1%20if%20no%20such%20k%20exists)
            * [prog.sf](./oeis-research/Thomas%20Ordowski/Smallest%20k%20such%20that%202^(2^n+1)-1%20+%202^k%20is%20prime,%20or%20-1%20if%20no%20such%20k%20exists/prog.sf)
        * [Smallest number k with n prime factors such that d + k over d is prime for every d | k](./oeis-research/Thomas%20Ordowski/Smallest%20number%20k%20with%20n%20prime%20factors%20such%20that%20d%20+%20k%20over%20d%20is%20prime%20for%20every%20d%20|%20k)
            * [generate.pl](./oeis-research/Thomas%20Ordowski/Smallest%20number%20k%20with%20n%20prime%20factors%20such%20that%20d%20+%20k%20over%20d%20is%20prime%20for%20every%20d%20|%20k/generate.pl)
        * [Super-poulet conjecture](./oeis-research/Thomas%20Ordowski/Super-poulet%20conjecture)
            * [super-poulet conjecture thomas.pl](./oeis-research/Thomas%20Ordowski/Super-poulet%20conjecture/super-poulet_conjecture_thomas.pl)
        * [Thomasz a and b sequences](./oeis-research/Thomas%20Ordowski/Thomasz%20a%20and%20b%20sequences)
            * [3-factors.pl](./oeis-research/Thomas%20Ordowski/Thomasz%20a%20and%20b%20sequences/3-factors.pl)
            * [conjecture.pl](./oeis-research/Thomas%20Ordowski/Thomasz%20a%20and%20b%20sequences/conjecture.pl)
            * [mail.sf](./oeis-research/Thomas%20Ordowski/Thomasz%20a%20and%20b%20sequences/mail.sf)
            * [negative jacobi.pl](./oeis-research/Thomas%20Ordowski/Thomasz%20a%20and%20b%20sequences/negative_jacobi.pl)
            * [pseudoprime search.pl](./oeis-research/Thomas%20Ordowski/Thomasz%20a%20and%20b%20sequences/pseudoprime_search.pl)
            * [solovay-strassen bounds.pl](./oeis-research/Thomas%20Ordowski/Thomasz%20a%20and%20b%20sequences/solovay-strassen_bounds.pl)
            * [upper-bounds with residue.pl](./oeis-research/Thomas%20Ordowski/Thomasz%20a%20and%20b%20sequences/upper-bounds_with_residue.pl)
            * [x.pl](./oeis-research/Thomas%20Ordowski/Thomasz%20a%20and%20b%20sequences/x.pl)
        * [Tomasz base = 5 primes](./oeis-research/Thomas%20Ordowski/Tomasz%20base%20=%205%20primes)
            * [prog.pl](./oeis-research/Thomas%20Ordowski/Tomasz%20base%20=%205%20primes/prog.pl)
            * [s.pl](./oeis-research/Thomas%20Ordowski/Tomasz%20base%20=%205%20primes/s.pl)
        * [Tomasz mod 1 divisors](./oeis-research/Thomas%20Ordowski/Tomasz%20mod%201%20divisors)
            * [find terms.sf](./oeis-research/Thomas%20Ordowski/Tomasz%20mod%201%20divisors/find_terms.sf)
            * [tomasz 5731 evidence.sf](./oeis-research/Thomas%20Ordowski/Tomasz%20mod%201%20divisors/tomasz_5731_evidence.sf)
        * [Tomasz new sequences](./oeis-research/Thomas%20Ordowski/Tomasz%20new%20sequences)
            * [ab prime.sf](./oeis-research/Thomas%20Ordowski/Tomasz%20new%20sequences/ab_prime.sf)
            * [conjecture new.pl](./oeis-research/Thomas%20Ordowski/Tomasz%20new%20sequences/conjecture_new.pl)
            * [isok.pl](./oeis-research/Thomas%20Ordowski/Tomasz%20new%20sequences/isok.pl)
            * [isok.sf](./oeis-research/Thomas%20Ordowski/Tomasz%20new%20sequences/isok.sf)
            * [prog.pl](./oeis-research/Thomas%20Ordowski/Tomasz%20new%20sequences/prog.pl)
            * [prog.sf](./oeis-research/Thomas%20Ordowski/Tomasz%20new%20sequences/prog.sf)
            * [pseudoprime search.pl](./oeis-research/Thomas%20Ordowski/Tomasz%20new%20sequences/pseudoprime_search.pl)
            * [upper-bounds with residue.pl](./oeis-research/Thomas%20Ordowski/Tomasz%20new%20sequences/upper-bounds_with_residue.pl)
            * [wrong conjecture.pl](./oeis-research/Thomas%20Ordowski/Tomasz%20new%20sequences/wrong_conjecture.pl)
        * [Tomasz p+1 semiprimes](./oeis-research/Thomas%20Ordowski/Tomasz%20p+1%20semiprimes)
            * [prog.pl](./oeis-research/Thomas%20Ordowski/Tomasz%20p+1%20semiprimes/prog.pl)
        * [Tomasz rad p+1 pseudoprimes](./oeis-research/Thomas%20Ordowski/Tomasz%20rad%20p+1%20pseudoprimes)
            * [bf.sf](./oeis-research/Thomas%20Ordowski/Tomasz%20rad%20p+1%20pseudoprimes/bf.sf)
            * [generate.pl](./oeis-research/Thomas%20Ordowski/Tomasz%20rad%20p+1%20pseudoprimes/generate.pl)
            * [generate special form.pl](./oeis-research/Thomas%20Ordowski/Tomasz%20rad%20p+1%20pseudoprimes/generate_special_form.pl)
            * [pseudoprimes testing.pl](./oeis-research/Thomas%20Ordowski/Tomasz%20rad%20p+1%20pseudoprimes/pseudoprimes_testing.pl)
            * [smooth.pl](./oeis-research/Thomas%20Ordowski/Tomasz%20rad%20p+1%20pseudoprimes/smooth.pl)
        * [Tomasz rad p-1 pseudoprimes](./oeis-research/Thomas%20Ordowski/Tomasz%20rad%20p-1%20pseudoprimes)
            * [generate.pl](./oeis-research/Thomas%20Ordowski/Tomasz%20rad%20p-1%20pseudoprimes/generate.pl)
            * [generate special form.pl](./oeis-research/Thomas%20Ordowski/Tomasz%20rad%20p-1%20pseudoprimes/generate_special_form.pl)
        * [Tomasz squarefree conjecture](./oeis-research/Thomas%20Ordowski/Tomasz%20squarefree%20conjecture)
            * [prog.sf](./oeis-research/Thomas%20Ordowski/Tomasz%20squarefree%20conjecture/prog.sf)
        * [Tomazs znorder primes](./oeis-research/Thomas%20Ordowski/Tomazs%20znorder%20primes)
            * [prog.pl](./oeis-research/Thomas%20Ordowski/Tomazs%20znorder%20primes/prog.pl)
    * [Tim Johannes Ohrtmann](./oeis-research/Tim%20Johannes%20Ohrtmann)
        * [Least Carmichael number that is divisible by the n-th cyclic number A003277(n), or 0 if no such number exists](./oeis-research/Tim%20Johannes%20Ohrtmann/Least%20Carmichael%20number%20that%20is%20divisible%20by%20the%20n-th%20cyclic%20number%20A003277(n),%20or%200%20if%20no%20such%20number%20exists)
            * [prog.pl](./oeis-research/Tim%20Johannes%20Ohrtmann/Least%20Carmichael%20number%20that%20is%20divisible%20by%20the%20n-th%20cyclic%20number%20A003277(n),%20or%200%20if%20no%20such%20number%20exists/prog.pl)
        * [Least Lucas-Carmichael number which is divisible by b(n), where {b(n)} (A255602) is the list of all numbers which could be a divisor of a Lucas-Carmichael number](./oeis-research/Tim%20Johannes%20Ohrtmann/Least%20Lucas-Carmichael%20number%20which%20is%20divisible%20by%20b(n),%20where%20{b(n)}%20(A255602)%20is%20the%20list%20of%20all%20numbers%20which%20could%20be%20a%20divisor%20of%20a%20Lucas-Carmichael%20number)
            * [find a155.pl](./oeis-research/Tim%20Johannes%20Ohrtmann/Least%20Lucas-Carmichael%20number%20which%20is%20divisible%20by%20b(n),%20where%20{b(n)}%20(A255602)%20is%20the%20list%20of%20all%20numbers%20which%20could%20be%20a%20divisor%20of%20a%20Lucas-Carmichael%20number/find_a155.pl)
            * [find upper bounds.sf](./oeis-research/Tim%20Johannes%20Ohrtmann/Least%20Lucas-Carmichael%20number%20which%20is%20divisible%20by%20b(n),%20where%20{b(n)}%20(A255602)%20is%20the%20list%20of%20all%20numbers%20which%20could%20be%20a%20divisor%20of%20a%20Lucas-Carmichael%20number/find_upper_bounds.sf)
            * [generate.pl](./oeis-research/Tim%20Johannes%20Ohrtmann/Least%20Lucas-Carmichael%20number%20which%20is%20divisible%20by%20b(n),%20where%20{b(n)}%20(A255602)%20is%20the%20list%20of%20all%20numbers%20which%20could%20be%20a%20divisor%20of%20a%20Lucas-Carmichael%20number/generate.pl)
            * [generate faster.pl](./oeis-research/Tim%20Johannes%20Ohrtmann/Least%20Lucas-Carmichael%20number%20which%20is%20divisible%20by%20b(n),%20where%20{b(n)}%20(A255602)%20is%20the%20list%20of%20all%20numbers%20which%20could%20be%20a%20divisor%20of%20a%20Lucas-Carmichael%20number/generate_faster.pl)
            * [prog.pl](./oeis-research/Tim%20Johannes%20Ohrtmann/Least%20Lucas-Carmichael%20number%20which%20is%20divisible%20by%20b(n),%20where%20{b(n)}%20(A255602)%20is%20the%20list%20of%20all%20numbers%20which%20could%20be%20a%20divisor%20of%20a%20Lucas-Carmichael%20number/prog.pl)
            * [upper-bounds.pl](./oeis-research/Tim%20Johannes%20Ohrtmann/Least%20Lucas-Carmichael%20number%20which%20is%20divisible%20by%20b(n),%20where%20{b(n)}%20(A255602)%20is%20the%20list%20of%20all%20numbers%20which%20could%20be%20a%20divisor%20of%20a%20Lucas-Carmichael%20number/upper-bounds.pl)
            * [verify bfile.sf](./oeis-research/Tim%20Johannes%20Ohrtmann/Least%20Lucas-Carmichael%20number%20which%20is%20divisible%20by%20b(n),%20where%20{b(n)}%20(A255602)%20is%20the%20list%20of%20all%20numbers%20which%20could%20be%20a%20divisor%20of%20a%20Lucas-Carmichael%20number/verify_bfile.sf)
        * [Least Lucas-Carmichael number with n prime factors](./oeis-research/Tim%20Johannes%20Ohrtmann/Least%20Lucas-Carmichael%20number%20with%20n%20prime%20factors)
            * [prog.pl](./oeis-research/Tim%20Johannes%20Ohrtmann/Least%20Lucas-Carmichael%20number%20with%20n%20prime%20factors/prog.pl)
            * [prog.sf](./oeis-research/Tim%20Johannes%20Ohrtmann/Least%20Lucas-Carmichael%20number%20with%20n%20prime%20factors/prog.sf)
        * [Number of eleven-prime Carmichael numbers less than 10^n](./oeis-research/Tim%20Johannes%20Ohrtmann/Number%20of%20eleven-prime%20Carmichael%20numbers%20less%20than%2010^n)
            * [prog.pl](./oeis-research/Tim%20Johannes%20Ohrtmann/Number%20of%20eleven-prime%20Carmichael%20numbers%20less%20than%2010^n/prog.pl)
        * [Number of Lucas-Carmichael numbers less than 10^n](./oeis-research/Tim%20Johannes%20Ohrtmann/Number%20of%20Lucas-Carmichael%20numbers%20less%20than%2010^n)
            * [prog.sf](./oeis-research/Tim%20Johannes%20Ohrtmann/Number%20of%20Lucas-Carmichael%20numbers%20less%20than%2010^n/prog.sf)
        * [Numbers n such that (9^n + 7^n) ÷ 16 is prime](./oeis-research/Tim%20Johannes%20Ohrtmann/Numbers%20n%20such%20that%20(9^n%20+%207^n)%20÷%2016%20is%20prime)
            * [prog.sf](./oeis-research/Tim%20Johannes%20Ohrtmann/Numbers%20n%20such%20that%20(9^n%20+%207^n)%20÷%2016%20is%20prime/prog.sf)
    * [Tomohiro Yamada](./oeis-research/Tomohiro%20Yamada)
        * [Quadratically perfect numbers](./oeis-research/Tomohiro%20Yamada/Quadratically%20perfect%20numbers)
            * [prog.pl](./oeis-research/Tomohiro%20Yamada/Quadratically%20perfect%20numbers/prog.pl)
            * [prog.sf](./oeis-research/Tomohiro%20Yamada/Quadratically%20perfect%20numbers/prog.sf)
    * [Tony Davie](./oeis-research/Tony%20Davie)
        * [Numbers n such that 2^n + 5 is prime](./oeis-research/Tony%20Davie/Numbers%20n%20such%20that%202^n%20+%205%20is%20prime)
            * [prog.pl](./oeis-research/Tony%20Davie/Numbers%20n%20such%20that%202^n%20+%205%20is%20prime/prog.pl)
    * [Torbjorn Alm](./oeis-research/Torbjorn%20Alm)
        * [A(n) is the largest prime factor of (n-1)^n - n^(n-1)](./oeis-research/Torbjorn%20Alm/a(n)%20is%20the%20largest%20prime%20factor%20of%20(n-1)^n%20-%20n^(n-1))
            * [prog.sf](./oeis-research/Torbjorn%20Alm/a(n)%20is%20the%20largest%20prime%20factor%20of%20(n-1)^n%20-%20n^(n-1)/prog.sf)
    * [Vincenzo Librandi](./oeis-research/Vincenzo%20Librandi)
        * [Numbers k such that (2^k-k+1)*2^k+1 is a semiprime](./oeis-research/Vincenzo%20Librandi/Numbers%20k%20such%20that%20(2^k-k+1)*2^k+1%20is%20a%20semiprime)
            * [prog.sf](./oeis-research/Vincenzo%20Librandi/Numbers%20k%20such%20that%20(2^k-k+1)*2^k+1%20is%20a%20semiprime/prog.sf)
        * [Numbers k such that 3^k + k - 1 is a prime](./oeis-research/Vincenzo%20Librandi/Numbers%20k%20such%20that%203^k%20+%20k%20-%201%20is%20a%20prime)
            * [prog.pl](./oeis-research/Vincenzo%20Librandi/Numbers%20k%20such%20that%203^k%20+%20k%20-%201%20is%20a%20prime/prog.pl)
        * [Numbers k such that 7^k+5^k+1 is prime](./oeis-research/Vincenzo%20Librandi/Numbers%20k%20such%20that%207^k+5^k+1%20is%20prime)
            * [prog.sf](./oeis-research/Vincenzo%20Librandi/Numbers%20k%20such%20that%207^k+5^k+1%20is%20prime/prog.sf)
    * [Vladimir Letsko](./oeis-research/Vladimir%20Letsko)
        * [The least k such that i*k + 1 is a product of i (not necessary distinct) primes for i = 1..n](./oeis-research/Vladimir%20Letsko/The%20least%20k%20such%20that%20i*k%20+%201%20is%20a%20product%20of%20i%20(not%20necessary%20distinct)%20primes%20for%20i%20=%201..n)
            * [prog.pl](./oeis-research/Vladimir%20Letsko/The%20least%20k%20such%20that%20i*k%20+%201%20is%20a%20product%20of%20i%20(not%20necessary%20distinct)%20primes%20for%20i%20=%201..n/prog.pl)
        * [The least k such that i*k + 1 is a product of i different primes for i = 1..n](./oeis-research/Vladimir%20Letsko/The%20least%20k%20such%20that%20i*k%20+%201%20is%20a%20product%20of%20i%20different%20primes%20for%20i%20=%201..n)
            * [prog.pl](./oeis-research/Vladimir%20Letsko/The%20least%20k%20such%20that%20i*k%20+%201%20is%20a%20product%20of%20i%20different%20primes%20for%20i%20=%201..n/prog.pl)
    * [Vladimir Shevelev](./oeis-research/Vladimir%20Shevelev)
        * [Numbers m such that both numbers 2^m +- 1 have at most 2 distinct prime factors](./oeis-research/Vladimir%20Shevelev/Numbers%20m%20such%20that%20both%20numbers%202^m%20+-%201%20have%20at%20most%202%20distinct%20prime%20factors)
            * [prog.sf](./oeis-research/Vladimir%20Shevelev/Numbers%20m%20such%20that%20both%20numbers%202^m%20+-%201%20have%20at%20most%202%20distinct%20prime%20factors/prog.sf)
    * [Wesley Ivan Hurt](./oeis-research/Wesley%20Ivan%20Hurt)
        * [Number of distinct prime factors of sigma n(n)](./oeis-research/Wesley%20Ivan%20Hurt/Number%20of%20distinct%20prime%20factors%20of%20sigma_n(n))
            * [factorizations.sf](./oeis-research/Wesley%20Ivan%20Hurt/Number%20of%20distinct%20prime%20factors%20of%20sigma_n(n)/factorizations.sf)
            * [prog.sf](./oeis-research/Wesley%20Ivan%20Hurt/Number%20of%20distinct%20prime%20factors%20of%20sigma_n(n)/prog.sf)
        * [Sum of denominators sequences](./oeis-research/Wesley%20Ivan%20Hurt/Sum%20of%20denominators%20sequences)
            * [A279911.sf](./oeis-research/Wesley%20Ivan%20Hurt/Sum%20of%20denominators%20sequences/A279911.sf)
            * [A279912.sf](./oeis-research/Wesley%20Ivan%20Hurt/Sum%20of%20denominators%20sequences/A279912.sf)
            * [connection to cyclotomic polynomials.sf](./oeis-research/Wesley%20Ivan%20Hurt/Sum%20of%20denominators%20sequences/connection_to_cyclotomic_polynomials.sf)
        * [Sum of the divisors of sigma n(n)](./oeis-research/Wesley%20Ivan%20Hurt/Sum%20of%20the%20divisors%20of%20sigma_n(n))
            * [prog.sf](./oeis-research/Wesley%20Ivan%20Hurt/Sum%20of%20the%20divisors%20of%20sigma_n(n)/prog.sf)
    * [Ya-Ping Lu](./oeis-research/Ya-Ping%20Lu)
        * [Integers m such that 20^m*(5^(m+1) - 1) div 4 + (20^m - 1) div 19 is a prime](./oeis-research/Ya-Ping%20Lu/Integers%20m%20such%20that%2020^m*(5^(m+1)%20-%201)%20div%204%20+%20(20^m%20-%201)%20div%2019%20is%20a%20prime)
            * [search.sf](./oeis-research/Ya-Ping%20Lu/Integers%20m%20such%20that%2020^m*(5^(m+1)%20-%201)%20div%204%20+%20(20^m%20-%201)%20div%2019%20is%20a%20prime/search.sf)
    * [Yasutoshi Kohmoto](./oeis-research/Yasutoshi%20Kohmoto)
        * [A(0) = 1, a(n) is the greatest prime factor of a(n-1)^2+1 for n > 0](./oeis-research/Yasutoshi%20Kohmoto/a(0)%20=%201,%20a(n)%20is%20the%20greatest%20prime%20factor%20of%20a(n-1)^2+1%20for%20n%20>%200)
            * [prog.sf](./oeis-research/Yasutoshi%20Kohmoto/a(0)%20=%201,%20a(n)%20is%20the%20greatest%20prime%20factor%20of%20a(n-1)^2+1%20for%20n%20>%200/prog.sf)
    * [Yusuf Gurtas](./oeis-research/Yusuf%20Gurtas)
        * [Smallest prime p for which the absolute value of the difference between the numbers of distinct prime factors of p+1 and p-1 is exactly n](./oeis-research/Yusuf%20Gurtas/Smallest%20prime%20p%20for%20which%20the%20absolute%20value%20of%20the%20difference%20between%20the%20numbers%20of%20distinct%20prime%20factors%20of%20p+1%20and%20p-1%20is%20exactly%20n)
            * [upper-bounds.sf](./oeis-research/Yusuf%20Gurtas/Smallest%20prime%20p%20for%20which%20the%20absolute%20value%20of%20the%20difference%20between%20the%20numbers%20of%20distinct%20prime%20factors%20of%20p+1%20and%20p-1%20is%20exactly%20n/upper-bounds.sf)
    * [Zak Seidov](./oeis-research/Zak%20Seidov)
        * [6^n is the sum of two consecutive primes](./oeis-research/Zak%20Seidov/6^n%20is%20the%20sum%20of%20two%20consecutive%20primes)
            * [2n.pl](./oeis-research/Zak%20Seidov/6^n%20is%20the%20sum%20of%20two%20consecutive%20primes/2n.pl)
            * [3n.pl](./oeis-research/Zak%20Seidov/6^n%20is%20the%20sum%20of%20two%20consecutive%20primes/3n.pl)
            * [6n.pl](./oeis-research/Zak%20Seidov/6^n%20is%20the%20sum%20of%20two%20consecutive%20primes/6n.pl)
        * [A(n) = sigma 2(a(n-1)), with a(1) = 2](./oeis-research/Zak%20Seidov/a(n)%20=%20sigma_2(a(n-1)),%20with%20a(1)%20=%202)
            * [factorization of a(16).sf](./oeis-research/Zak%20Seidov/a(n)%20=%20sigma_2(a(n-1)),%20with%20a(1)%20=%202/factorization_of_a(16).sf)
            * [filter composites.sf](./oeis-research/Zak%20Seidov/a(n)%20=%20sigma_2(a(n-1)),%20with%20a(1)%20=%202/filter_composites.sf)
            * [prog.sf](./oeis-research/Zak%20Seidov/a(n)%20=%20sigma_2(a(n-1)),%20with%20a(1)%20=%202/prog.sf)
            * [sigma factors of a(17).sf](./oeis-research/Zak%20Seidov/a(n)%20=%20sigma_2(a(n-1)),%20with%20a(1)%20=%202/sigma_factors_of_a(17).sf)
        * [A(n) is the least k > a(n-1) such that k - a(i) for i = 0 .. n-1 all have exactly n prime factors, counted with multiplicity; a(0) = 0](./oeis-research/Zak%20Seidov/a(n)%20is%20the%20least%20k%20>%20a(n-1)%20such%20that%20k%20-%20a(i)%20for%20i%20=%200%20..%20n-1%20all%20have%20exactly%20n%20prime%20factors,%20counted%20with%20multiplicity;%20a(0)%20=%200)
            * [generate.pl](./oeis-research/Zak%20Seidov/a(n)%20is%20the%20least%20k%20>%20a(n-1)%20such%20that%20k%20-%20a(i)%20for%20i%20=%200%20..%20n-1%20all%20have%20exactly%20n%20prime%20factors,%20counted%20with%20multiplicity;%20a(0)%20=%200/generate.pl)
        * [A(n) is the least odd number k such that Omega(k) = n, Omega(k+2) = n+1, and Omega(k+4) = n+2](./oeis-research/Zak%20Seidov/a(n)%20is%20the%20least%20odd%20number%20k%20such%20that%20Omega(k)%20=%20n,%20Omega(k+2)%20=%20n+1,%20and%20Omega(k+4)%20=%20n+2)
            * [generate.pl](./oeis-research/Zak%20Seidov/a(n)%20is%20the%20least%20odd%20number%20k%20such%20that%20Omega(k)%20=%20n,%20Omega(k+2)%20=%20n+1,%20and%20Omega(k+4)%20=%20n+2/generate.pl)
        * [A(n) is the smallest even number k such that k-1 and k+1 are both n-almost primes](./oeis-research/Zak%20Seidov/a(n)%20is%20the%20smallest%20even%20number%20k%20such%20that%20k-1%20and%20k+1%20are%20both%20n-almost%20primes)
            * [generate.pl](./oeis-research/Zak%20Seidov/a(n)%20is%20the%20smallest%20even%20number%20k%20such%20that%20k-1%20and%20k+1%20are%20both%20n-almost%20primes/generate.pl)
            * [prog ntheory.pl](./oeis-research/Zak%20Seidov/a(n)%20is%20the%20smallest%20even%20number%20k%20such%20that%20k-1%20and%20k+1%20are%20both%20n-almost%20primes/prog_ntheory.pl)
        * [A(n) is the smallest number m such that m, m+1, m+2 and m+3 each have exactly n prime factors (counted with multiplicity)](./oeis-research/Zak%20Seidov/a(n)%20is%20the%20smallest%20number%20m%20such%20that%20m,%20m+1,%20m+2%20and%20m+3%20each%20have%20exactly%20n%20prime%20factors%20(counted%20with%20multiplicity))
            * [prog.sf](./oeis-research/Zak%20Seidov/a(n)%20is%20the%20smallest%20number%20m%20such%20that%20m,%20m+1,%20m+2%20and%20m+3%20each%20have%20exactly%20n%20prime%20factors%20(counted%20with%20multiplicity)/prog.sf)
        * [Concatenation of numbers from n to a(n) is prime](./oeis-research/Zak%20Seidov/Concatenation%20of%20numbers%20from%20n%20to%20a(n)%20is%20prime)
            * [prog.pl](./oeis-research/Zak%20Seidov/Concatenation%20of%20numbers%20from%20n%20to%20a(n)%20is%20prime/prog.pl)
        * [First n-almost prime after 3^n](./oeis-research/Zak%20Seidov/First%20n-almost%20prime%20after%203^n)
            * [next almost prime.sf](./oeis-research/Zak%20Seidov/First%20n-almost%20prime%20after%203^n/next_almost_prime.sf)
            * [search.pl](./oeis-research/Zak%20Seidov/First%20n-almost%20prime%20after%203^n/search.pl)
        * [First number k such that Omega(k) = n and Omega(n - 1) = Omega(n + 1) = n + 1](./oeis-research/Zak%20Seidov/First%20number%20k%20such%20that%20Omega(k)%20=%20n%20and%20Omega(n%20-%201)%20=%20Omega(n%20+%201)%20=%20n%20+%201)
            * [generate.pl](./oeis-research/Zak%20Seidov/First%20number%20k%20such%20that%20Omega(k)%20=%20n%20and%20Omega(n%20-%201)%20=%20Omega(n%20+%201)%20=%20n%20+%201/generate.pl)
        * [First prime p such that, if q are r are the next two primes, p + r, p + q, q + r and p + q + r all have n prime divisors, counted with multiplicity](./oeis-research/Zak%20Seidov/First%20prime%20p%20such%20that,%20if%20q%20are%20r%20are%20the%20next%20two%20primes,%20p%20+%20r,%20p%20+%20q,%20q%20+%20r%20and%20p%20+%20q%20+%20r%20all%20have%20n%20prime%20divisors,%20counted%20with%20multiplicity)
            * [almost prime generation.pl](./oeis-research/Zak%20Seidov/First%20prime%20p%20such%20that,%20if%20q%20are%20r%20are%20the%20next%20two%20primes,%20p%20+%20r,%20p%20+%20q,%20q%20+%20r%20and%20p%20+%20q%20+%20r%20all%20have%20n%20prime%20divisors,%20counted%20with%20multiplicity/almost_prime_generation.pl)
            * [prog faster.pl](./oeis-research/Zak%20Seidov/First%20prime%20p%20such%20that,%20if%20q%20are%20r%20are%20the%20next%20two%20primes,%20p%20+%20r,%20p%20+%20q,%20q%20+%20r%20and%20p%20+%20q%20+%20r%20all%20have%20n%20prime%20divisors,%20counted%20with%20multiplicity/prog_faster.pl)
        * [Least k that starts a sequence of exactly n numbers on which i + Omega(i) is constant](./oeis-research/Zak%20Seidov/Least%20k%20that%20starts%20a%20sequence%20of%20exactly%20n%20numbers%20on%20which%20i%20+%20Omega(i)%20is%20constant)
            * [generate.pl](./oeis-research/Zak%20Seidov/Least%20k%20that%20starts%20a%20sequence%20of%20exactly%20n%20numbers%20on%20which%20i%20+%20Omega(i)%20is%20constant/generate.pl)
            * [upper-bounds.pl](./oeis-research/Zak%20Seidov/Least%20k%20that%20starts%20a%20sequence%20of%20exactly%20n%20numbers%20on%20which%20i%20+%20Omega(i)%20is%20constant/upper-bounds.pl)
        * [Least number k such that 3^k-2 and 3^k+2 are the product of n prime factors counted with multiplicity](./oeis-research/Zak%20Seidov/Least%20number%20k%20such%20that%203^k-2%20and%203^k+2%20are%20the%20product%20of%20n%20prime%20factors%20counted%20with%20multiplicity)
            * [prog.sf](./oeis-research/Zak%20Seidov/Least%20number%20k%20such%20that%203^k-2%20and%203^k+2%20are%20the%20product%20of%20n%20prime%20factors%20counted%20with%20multiplicity/prog.sf)
        * [Least number k such that both prime(k+1) +- prime(k) are products of n prime factors (counting multiplicity)](./oeis-research/Zak%20Seidov/Least%20number%20k%20such%20that%20both%20prime(k+1)%20+-%20prime(k)%20are%20products%20of%20n%20prime%20factors%20(counting%20multiplicity))
            * [prog.pl](./oeis-research/Zak%20Seidov/Least%20number%20k%20such%20that%20both%20prime(k+1)%20+-%20prime(k)%20are%20products%20of%20n%20prime%20factors%20(counting%20multiplicity)/prog.pl)
            * [sieve.pl](./oeis-research/Zak%20Seidov/Least%20number%20k%20such%20that%20both%20prime(k+1)%20+-%20prime(k)%20are%20products%20of%20n%20prime%20factors%20(counting%20multiplicity)/sieve.pl)
        * [Least number k such that k, k -'s and k +'s all have n prime divisors, counted with multiplicity, where's is the sum of the decimal digits of k](./oeis-research/Zak%20Seidov/Least%20number%20k%20such%20that%20k,%20k%20-%20s%20and%20k%20+%20s%20all%20have%20n%20prime%20divisors,%20counted%20with%20multiplicity,%20where%20s%20is%20the%20sum%20of%20the%20decimal%20digits%20of%20k)
            * [generate.pl](./oeis-research/Zak%20Seidov/Least%20number%20k%20such%20that%20k,%20k%20-%20s%20and%20k%20+%20s%20all%20have%20n%20prime%20divisors,%20counted%20with%20multiplicity,%20where%20s%20is%20the%20sum%20of%20the%20decimal%20digits%20of%20k/generate.pl)
        * [Least odd number k such that Omega(k) = n, Omega(k+2) = n+1, and Omega(k+4) = n+2](./oeis-research/Zak%20Seidov/Least%20odd%20number%20k%20such%20that%20Omega(k)%20=%20n,%20Omega(k+2)%20=%20n+1,%20and%20Omega(k+4)%20=%20n+2)
            * [prog.pl](./oeis-research/Zak%20Seidov/Least%20odd%20number%20k%20such%20that%20Omega(k)%20=%20n,%20Omega(k+2)%20=%20n+1,%20and%20Omega(k+4)%20=%20n+2/prog.pl)
        * [Least prime p such that the concatenation p|n has exactly n prime factors with multiplicity](./oeis-research/Zak%20Seidov/Least%20prime%20p%20such%20that%20the%20concatenation%20p|n%20has%20exactly%20n%20prime%20factors%20with%20multiplicity)
            * [prog.pl](./oeis-research/Zak%20Seidov/Least%20prime%20p%20such%20that%20the%20concatenation%20p|n%20has%20exactly%20n%20prime%20factors%20with%20multiplicity/prog.pl)
            * [prog.sf](./oeis-research/Zak%20Seidov/Least%20prime%20p%20such%20that%20the%20concatenation%20p|n%20has%20exactly%20n%20prime%20factors%20with%20multiplicity/prog.sf)
        * [Least prime p such that x^2 + 3*x + p produces primes for x = 0..n-1 but not x = n](./oeis-research/Zak%20Seidov/Least%20prime%20p%20such%20that%20x^2%20+%203*x%20+%20p%20produces%20primes%20for%20x%20=%200..n-1%20but%20not%20x%20=%20n)
            * [sieve.pl](./oeis-research/Zak%20Seidov/Least%20prime%20p%20such%20that%20x^2%20+%203*x%20+%20p%20produces%20primes%20for%20x%20=%200..n-1%20but%20not%20x%20=%20n/sieve.pl)
        * [Numbers k that are the sum and product of 5 consecutive primes](./oeis-research/Zak%20Seidov/Numbers%20k%20that%20are%20the%20sum%20and%20product%20of%205%20consecutive%20primes)
            * [prog.pl](./oeis-research/Zak%20Seidov/Numbers%20k%20that%20are%20the%20sum%20and%20product%20of%205%20consecutive%20primes/prog.pl)
            * [prog.sf](./oeis-research/Zak%20Seidov/Numbers%20k%20that%20are%20the%20sum%20and%20product%20of%205%20consecutive%20primes/prog.sf)
            * [prog check.sf](./oeis-research/Zak%20Seidov/Numbers%20k%20that%20are%20the%20sum%20and%20product%20of%205%20consecutive%20primes/prog_check.sf)
        * [Prev prime and next prime same nr of factors](./oeis-research/Zak%20Seidov/Prev%20prime%20and%20next%20prime%20same%20nr%20of%20factors)
            * [prog.pl](./oeis-research/Zak%20Seidov/Prev%20prime%20and%20next%20prime%20same%20nr%20of%20factors/prog.pl)
        * [Primes p congruent to 1..10 mod 11](./oeis-research/Zak%20Seidov/Primes%20p%20congruent%20to%201..10%20mod%2011)
            * [check.sf](./oeis-research/Zak%20Seidov/Primes%20p%20congruent%20to%201..10%20mod%2011/check.sf)
            * [search.pl](./oeis-research/Zak%20Seidov/Primes%20p%20congruent%20to%201..10%20mod%2011/search.pl)
            * [sieve cluster.pl](./oeis-research/Zak%20Seidov/Primes%20p%20congruent%20to%201..10%20mod%2011/sieve_cluster.pl)
        * [Primes p congruent to 1..8 mod 13](./oeis-research/Zak%20Seidov/Primes%20p%20congruent%20to%201..8%20mod%2013)
            * [check.sf](./oeis-research/Zak%20Seidov/Primes%20p%20congruent%20to%201..8%20mod%2013/check.sf)
            * [search.pl](./oeis-research/Zak%20Seidov/Primes%20p%20congruent%20to%201..8%20mod%2013/search.pl)
            * [sieve cluster.pl](./oeis-research/Zak%20Seidov/Primes%20p%20congruent%20to%201..8%20mod%2013/sieve_cluster.pl)
        * [Primes p such that p + m^2 is prime for all m in {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}](./oeis-research/Zak%20Seidov/Primes%20p%20such%20that%20p%20+%20m^2%20is%20prime%20for%20all%20m%20in%20{2,%204,%206,%208,%2010,%2012,%2014,%2016,%2018,%2020,%2022,%2024})
            * [sieve.sf](./oeis-research/Zak%20Seidov/Primes%20p%20such%20that%20p%20+%20m^2%20is%20prime%20for%20all%20m%20in%20{2,%204,%206,%208,%2010,%2012,%2014,%2016,%2018,%2020,%2022,%2024}/sieve.sf)
        * [Smallest prime p cogruent to 1..prime(n)-1 mod prime(n)](./oeis-research/Zak%20Seidov/Smallest%20prime%20p%20cogruent%20to%201..prime(n)-1%20mod%20prime(n))
            * [search.pl](./oeis-research/Zak%20Seidov/Smallest%20prime%20p%20cogruent%20to%201..prime(n)-1%20mod%20prime(n)/search.pl)
        * [Smallest prime p such that 2p+3q and 3p+2q are n-almost primes, where q is next prime after p](./oeis-research/Zak%20Seidov/Smallest%20prime%20p%20such%20that%202p+3q%20and%203p+2q%20are%20n-almost%20primes,%20where%20q%20is%20next%20prime%20after%20p)
            * [bruteforce.pl](./oeis-research/Zak%20Seidov/Smallest%20prime%20p%20such%20that%202p+3q%20and%203p+2q%20are%20n-almost%20primes,%20where%20q%20is%20next%20prime%20after%20p/bruteforce.pl)
            * [generate.pl](./oeis-research/Zak%20Seidov/Smallest%20prime%20p%20such%20that%202p+3q%20and%203p+2q%20are%20n-almost%20primes,%20where%20q%20is%20next%20prime%20after%20p/generate.pl)
    * [Zhao Hui Du](./oeis-research/Zhao%20Hui%20Du)
        * [Smallest integer k such that factorial(k) starts with the first n digits of Pi](./oeis-research/Zhao%20Hui%20Du/Smallest%20integer%20k%20such%20that%20factorial(k)%20starts%20with%20the%20first%20n%20digits%20of%20Pi)
            * [prog.sf](./oeis-research/Zhao%20Hui%20Du/Smallest%20integer%20k%20such%20that%20factorial(k)%20starts%20with%20the%20first%20n%20digits%20of%20Pi/prog.sf)
    * [Zhining Yang](./oeis-research/Zhining%20Yang)
        * [Positive numbers whose squares have at most one digit less than 8](./oeis-research/Zhining%20Yang/Positive%20numbers%20whose%20squares%20have%20at%20most%20one%20digit%20less%20than%208)
            * [prog.pl](./oeis-research/Zhining%20Yang/Positive%20numbers%20whose%20squares%20have%20at%20most%20one%20digit%20less%20than%208/prog.pl)
            * [prog.sf](./oeis-research/Zhining%20Yang/Positive%20numbers%20whose%20squares%20have%20at%20most%20one%20digit%20less%20than%208/prog.sf)
* [Pseudoprimes](./pseudoprimes)
    * [620-programs](./pseudoprimes/620-programs)
        * [$620 generation.sf](./pseudoprimes/620-programs/$620%20generation.sf)
        * [620 research.pl](./pseudoprimes/620-programs/620%20research.pl)
        * [620 research PSW.pl](./pseudoprimes/620-programs/620%20research_PSW.pl)
        * [620 fermat generator.pl](./pseudoprimes/620-programs/620_fermat_generator.pl)
        * [620 from big prime list.pl](./pseudoprimes/620-programs/620_from_big_prime_list.pl)
        * [620 from big prime list 2.pl](./pseudoprimes/620-programs/620_from_big_prime_list_2.pl)
        * [620 from big prime list 3.pl](./pseudoprimes/620-programs/620_from_big_prime_list_3.pl)
        * [620 lucas-fibonacci pseudoprimes.sf](./pseudoprimes/620-programs/620_lucas-fibonacci_pseudoprimes.sf)
        * [620 research with D.pl](./pseudoprimes/620-programs/620_research_with_D.pl)
        * [620 strong fermat generator.pl](./pseudoprimes/620-programs/620_strong_fermat_generator.pl)
        * [620 strong generator.pl](./pseudoprimes/620-programs/620_strong_generator.pl)
        * [carmichael euler phi.pl](./pseudoprimes/620-programs/carmichael_euler_phi.pl)
        * [carmichael pseudoprimes.sf](./pseudoprimes/620-programs/carmichael_pseudoprimes.sf)
        * [create primes.pl](./pseudoprimes/620-programs/create_primes.pl)
        * [create primes 2.pl](./pseudoprimes/620-programs/create_primes_2.pl)
        * [pseudoprimes comb.pl](./pseudoprimes/620-programs/pseudoprimes_comb.pl)
    * [Generators](./pseudoprimes/generators)
        * [almost strong fermat psp from multiple.pl](./pseudoprimes/generators/almost_strong_fermat_psp_from_multiple.pl)
        * [carmichael-lucas-carmichael from multiple recursive mpz.pl](./pseudoprimes/generators/carmichael-lucas-carmichael_from_multiple_recursive_mpz.pl)
        * [carmichael-lucas-carmichael from prime factors unbounded mpz.pl](./pseudoprimes/generators/carmichael-lucas-carmichael_from_prime_factors_unbounded_mpz.pl)
        * [carmichael-lucas-carmichael number generation mpz.pl](./pseudoprimes/generators/carmichael-lucas-carmichael_number_generation_mpz.pl)
        * [carmichael almost lucas-carmichael from prime factors.pl](./pseudoprimes/generators/carmichael_almost_lucas-carmichael_from_prime_factors.pl)
        * [carmichael from combinations.sf](./pseudoprimes/generators/carmichael_from_combinations.sf)
        * [carmichael from combinations of primes recursive mpz.pl](./pseudoprimes/generators/carmichael_from_combinations_of_primes_recursive_mpz.pl)
        * [carmichael from multiple recursive mpz.pl](./pseudoprimes/generators/carmichael_from_multiple_recursive_mpz.pl)
        * [carmichael generate.pl](./pseudoprimes/generators/carmichael_generate.pl)
        * [carmichael in range from prime factors.pl](./pseudoprimes/generators/carmichael_in_range_from_prime_factors.pl)
        * [carmichael large from prime factors.pl](./pseudoprimes/generators/carmichael_large_from_prime_factors.pl)
        * [carmichael numbers in range.pl](./pseudoprimes/generators/carmichael_numbers_in_range.pl)
        * [carmichael numbers in range with prefix.pl](./pseudoprimes/generators/carmichael_numbers_in_range_with_prefix.pl)
        * [carmichael numbers in range with prefix mpz.pl](./pseudoprimes/generators/carmichael_numbers_in_range_with_prefix_mpz.pl)
        * [carmichael numbers p==3 mod 80 in range.pl](./pseudoprimes/generators/carmichael_numbers_p==3_mod_80_in_range.pl)
        * [carmichael with n prime factors from prime factors.pl](./pseudoprimes/generators/carmichael_with_n_prime_factors_from_prime_factors.pl)
        * [erdos carmichael from lambdas.pl](./pseudoprimes/generators/erdos_carmichael_from_lambdas.pl)
        * [erdos carmichael generate from prefix.pl](./pseudoprimes/generators/erdos_carmichael_generate_from_prefix.pl)
        * [erdos carmichael with prefix from lambda.pl](./pseudoprimes/generators/erdos_carmichael_with_prefix_from_lambda.pl)
        * [erdos generate carmichael shuffle.pl](./pseudoprimes/generators/erdos_generate_carmichael_shuffle.pl)
        * [erdos generate carmichael with prefix.pl](./pseudoprimes/generators/erdos_generate_carmichael_with_prefix.pl)
        * [erdos generate carmichal.pl](./pseudoprimes/generators/erdos_generate_carmichal.pl)
        * [erdos generate fibonacci from lambdas.pl](./pseudoprimes/generators/erdos_generate_fibonacci_from_lambdas.pl)
        * [erdos lucas-carmichael from lambdas.pl](./pseudoprimes/generators/erdos_lucas-carmichael_from_lambdas.pl)
        * [erdos lucas-carmichael generation.pl](./pseudoprimes/generators/erdos_lucas-carmichael_generation.pl)
        * [erdos lucas-carmichael with prefix.pl](./pseudoprimes/generators/erdos_lucas-carmichael_with_prefix.pl)
        * [erdos special carmichael with multiple.pl](./pseudoprimes/generators/erdos_special_carmichael_with_multiple.pl)
        * [fermat from generated primes.pl](./pseudoprimes/generators/fermat_from_generated_primes.pl)
        * [fermat from lambdas.pl](./pseudoprimes/generators/fermat_from_lambdas.pl)
        * [fermat from lucas sequences.sf](./pseudoprimes/generators/fermat_from_lucas_sequences.sf)
        * [fermat pseudoprimes from prime factors with p+1 smooth.pl](./pseudoprimes/generators/fermat_pseudoprimes_from_prime_factors_with_p+1_smooth.pl)
        * [fermat pseudoprimes generation.jl](./pseudoprimes/generators/fermat_pseudoprimes_generation.jl)
        * [fermat pseudoprimes in range.pl](./pseudoprimes/generators/fermat_pseudoprimes_in_range.pl)
        * [fermat pseudoprimes in range with prefix.pl](./pseudoprimes/generators/fermat_pseudoprimes_in_range_with_prefix.pl)
        * [fermat pseudoprimes in range with prefix mpz.pl](./pseudoprimes/generators/fermat_pseudoprimes_in_range_with_prefix_mpz.pl)
        * [fermat pseudoprimes p==3 mod 80 in range.pl](./pseudoprimes/generators/fermat_pseudoprimes_p==3_mod_80_in_range.pl)
        * [fermat pseudoprimes with small znorder.sf](./pseudoprimes/generators/fermat_pseudoprimes_with_small_znorder.sf)
        * [fermat strong pseudoprimes from prime factors.pl](./pseudoprimes/generators/fermat_strong_pseudoprimes_from_prime_factors.pl)
        * [fermat superpseudoprimes from prime factors.pl](./pseudoprimes/generators/fermat_superpseudoprimes_from_prime_factors.pl)
        * [generate abundant carmichael numbers.pl](./pseudoprimes/generators/generate_abundant_carmichael_numbers.pl)
        * [generate carmichael-hebyshev pseudoprimes.pl](./pseudoprimes/generators/generate_carmichael-hebyshev_pseudoprimes.pl)
        * [generate carmichael cyclic multiple.pl](./pseudoprimes/generators/generate_carmichael_cyclic_multiple.pl)
        * [generate carmichael of second order.pl](./pseudoprimes/generators/generate_carmichael_of_second_order.pl)
        * [generate carmichael of second order 2.pl](./pseudoprimes/generators/generate_carmichael_of_second_order_2.pl)
        * [generate carmichael of second order 3.pl](./pseudoprimes/generators/generate_carmichael_of_second_order_3.pl)
        * [generate carmichael overpseudoprimes.pl](./pseudoprimes/generators/generate_carmichael_overpseudoprimes.pl)
        * [generate carmichael overpseudoprimes.sf](./pseudoprimes/generators/generate_carmichael_overpseudoprimes.sf)
        * [generate carmichael superpseudoprimes.pl](./pseudoprimes/generators/generate_carmichael_superpseudoprimes.pl)
        * [generate chebyshev pseudoprimes.pl](./pseudoprimes/generators/generate_chebyshev_pseudoprimes.pl)
        * [generate chernick-like carmichael numbers.sf](./pseudoprimes/generators/generate_chernick-like_carmichael_numbers.sf)
        * [generate fermat overpseudoprimes.pl](./pseudoprimes/generators/generate_fermat_overpseudoprimes.pl)
        * [generate fermat overpseudoprimes 2.pl](./pseudoprimes/generators/generate_fermat_overpseudoprimes_2.pl)
        * [generate fermat p==3 (mod 80).pl](./pseudoprimes/generators/generate_fermat_p==3_(mod%2080).pl)
        * [generate fermat pseudoprimes.pl](./pseudoprimes/generators/generate_fermat_pseudoprimes.pl)
        * [generate fermat psp from multiples.pl](./pseudoprimes/generators/generate_fermat_psp_from_multiples.pl)
        * [generate fermat psp from multiples v2.pl](./pseudoprimes/generators/generate_fermat_psp_from_multiples_v2.pl)
        * [generate fermat psp to multiple bases from prime factors.pl](./pseudoprimes/generators/generate_fermat_psp_to_multiple_bases_from_prime_factors.pl)
        * [generate fermat psp with 620 primes.pl](./pseudoprimes/generators/generate_fermat_psp_with_620_primes.pl)
        * [generate fermat superpseudoprimes.pl](./pseudoprimes/generators/generate_fermat_superpseudoprimes.pl)
        * [generate frobenius pseudoprimes.pl](./pseudoprimes/generators/generate_frobenius_pseudoprimes.pl)
        * [generate large carmichael with k factors.sf](./pseudoprimes/generators/generate_large_carmichael_with_k_factors.sf)
        * [generate lucas-carmichael multiple.pl](./pseudoprimes/generators/generate_lucas-carmichael_multiple.pl)
        * [generate lucas pseudoprimes.pl](./pseudoprimes/generators/generate_lucas_pseudoprimes.pl)
        * [generate psp from primorials.sf](./pseudoprimes/generators/generate_psp_from_primorials.sf)
        * [generate psp from primorials 2.sf](./pseudoprimes/generators/generate_psp_from_primorials_2.sf)
        * [generate psp from root.sf](./pseudoprimes/generators/generate_psp_from_root.sf)
        * [generate PSW counter-example.sf](./pseudoprimes/generators/generate_PSW_counter-example.sf)
        * [generate psw counter-example from prime factors.pl](./pseudoprimes/generators/generate_psw_counter-example_from_prime_factors.pl)
        * [generate williams number from prime factors.pl](./pseudoprimes/generators/generate_williams_number_from_prime_factors.pl)
        * [generate williams numbers.pl](./pseudoprimes/generators/generate_williams_numbers.pl)
        * [generate williams numbers.sf](./pseudoprimes/generators/generate_williams_numbers.sf)
        * [imprimitive carmichael.sf](./pseudoprimes/generators/imprimitive_carmichael.sf)
        * [imprimitive carmichael better.sf](./pseudoprimes/generators/imprimitive_carmichael_better.sf)
        * [imprimitive carmichael coin change.sf](./pseudoprimes/generators/imprimitive_carmichael_coin_change.sf)
        * [inverse znorder generation.sf](./pseudoprimes/generators/inverse_znorder_generation.sf)
        * [larger carmichael from carmichael.sf](./pseudoprimes/generators/larger_carmichael_from_carmichael.sf)
        * [larger carmichael from carmichael simple.sf](./pseudoprimes/generators/larger_carmichael_from_carmichael_simple.sf)
        * [larger fermat from fermat.sf](./pseudoprimes/generators/larger_fermat_from_fermat.sf)
        * [larger fermat from fermat simple.sf](./pseudoprimes/generators/larger_fermat_from_fermat_simple.sf)
        * [larger fermat from fermat with variations.sf](./pseudoprimes/generators/larger_fermat_from_fermat_with_variations.sf)
        * [lucas-carmichael.pl](./pseudoprimes/generators/lucas-carmichael.pl)
        * [lucas-carmichael from combinations.sf](./pseudoprimes/generators/lucas-carmichael_from_combinations.sf)
        * [lucas-carmichael in range from prime factors.pl](./pseudoprimes/generators/lucas-carmichael_in_range_from_prime_factors.pl)
        * [lucas-carmichael numbers in range.pl](./pseudoprimes/generators/lucas-carmichael_numbers_in_range.pl)
        * [lucas-carmichael unbounded from prime factors from lambdas.pl](./pseudoprimes/generators/lucas-carmichael_unbounded_from_prime_factors_from_lambdas.pl)
        * [lucas carmichael divisible by n.pl](./pseudoprimes/generators/lucas_carmichael_divisible_by_n.pl)
        * [lucas psp from lambdas.pl](./pseudoprimes/generators/lucas_psp_from_lambdas.pl)
        * [non-residue generate.pl](./pseudoprimes/generators/non-residue_generate.pl)
        * [odd abundant cyclic numbers.sf](./pseudoprimes/generators/odd_abundant_cyclic_numbers.sf)
        * [odd almost abundant cyclic numbers.sf](./pseudoprimes/generators/odd_almost_abundant_cyclic_numbers.sf)
        * [odd almost abundant lucas-cyclic numbers.sf](./pseudoprimes/generators/odd_almost_abundant_lucas-cyclic_numbers.sf)
        * [pomerance generate smooth primes.pl](./pseudoprimes/generators/pomerance_generate_smooth_primes.pl)
        * [psp from psp.pl](./pseudoprimes/generators/psp_from_psp.pl)
        * [psp from smooth primes.pl](./pseudoprimes/generators/psp_from_smooth_primes.pl)
        * [psp from smooth primes extra.pl](./pseudoprimes/generators/psp_from_smooth_primes_extra.pl)
        * [recursively generate carmichael.sf](./pseudoprimes/generators/recursively_generate_carmichael.sf)
        * [recursively generate fermat from znorder.sf](./pseudoprimes/generators/recursively_generate_fermat_from_znorder.sf)
        * [recursively generate fermat from znorder with variations.sf](./pseudoprimes/generators/recursively_generate_fermat_from_znorder_with_variations.sf)
        * [recursivley generate carmichael.pl](./pseudoprimes/generators/recursivley_generate_carmichael.pl)
        * [recursivley generate lucas psp.pl](./pseudoprimes/generators/recursivley_generate_lucas_psp.pl)
        * [search lucas-carmichael from multiple.pl](./pseudoprimes/generators/search_lucas-carmichael_from_multiple.pl)
        * [special form carmichael.sf](./pseudoprimes/generators/special_form_carmichael.sf)
        * [squarefree fermat pseudoprimes in range.pl](./pseudoprimes/generators/squarefree_fermat_pseudoprimes_in_range.pl)
        * [squarefree strong fermat psp with n prime factors.pl](./pseudoprimes/generators/squarefree_strong_fermat_psp_with_n_prime_factors.pl)
        * [strong carmichael with n prime factors from prime factors.pl](./pseudoprimes/generators/strong_carmichael_with_n_prime_factors_from_prime_factors.pl)
        * [strong fermat psp with n prime factors from prime factors.pl](./pseudoprimes/generators/strong_fermat_psp_with_n_prime_factors_from_prime_factors.pl)
        * [strong fermat psp with n prime factors from prime factors 2.pl](./pseudoprimes/generators/strong_fermat_psp_with_n_prime_factors_from_prime_factors_2.pl)
        * [super poulet pseudoprimes.pl](./pseudoprimes/generators/super_poulet_pseudoprimes.pl)
        * [super poulet pseudoprimes from prime file.pl](./pseudoprimes/generators/super_poulet_pseudoprimes_from_prime_file.pl)
        * [super poulet pseudoprimes with generated primes.pl](./pseudoprimes/generators/super_poulet_pseudoprimes_with_generated_primes.pl)
    * [Primes](./pseudoprimes/primes)
        * [generate.pl](./pseudoprimes/primes/generate.pl)
        * [lucas carmichael erdos method.sf](./pseudoprimes/primes/lucas_carmichael_erdos_method.sf)
        * [super poulet pseudoprimes from prime file.pl](./pseudoprimes/primes/super_poulet_pseudoprimes_from_prime_file.pl)
    * [Programs](./pseudoprimes/programs)
        * [2^(k-1) == (2*k + 1) (mod k^2).pl](./pseudoprimes/programs/2^(k-1)%20==%20(2*k%20+%201)%20(mod%20k^2).pl)
        * [2^(k-1) == (2*k + 1) (mod k^2) db.pl](./pseudoprimes/programs/2^(k-1)%20==%20(2*k%20+%201)%20(mod%20k^2)_db.pl)
        * [2^(k-1) == (2*k + 1) (mod k^2) primes db.pl](./pseudoprimes/programs/2^(k-1)%20==%20(2*k%20+%201)%20(mod%20k^2)_primes_db.pl)
        * [2n+1 is carmichael.pl](./pseudoprimes/programs/2n+1_is_carmichael.pl)
        * [abundancy index records psp2.pl](./pseudoprimes/programs/abundancy_index_records_psp2.pl)
        * [abundant carmichael.pl](./pseudoprimes/programs/abundant_carmichael.pl)
        * [abundant carmichael cached.pl](./pseudoprimes/programs/abundant_carmichael_cached.pl)
        * [abundant fermat pseudoprimes.pl](./pseudoprimes/programs/abundant_fermat_pseudoprimes.pl)
        * [abundant fermat pseudoprimes cached.pl](./pseudoprimes/programs/abundant_fermat_pseudoprimes_cached.pl)
        * [abundant lucas-carmichael.pl](./pseudoprimes/programs/abundant_lucas-carmichael.pl)
        * [abundant lucas-carmichael cached.pl](./pseudoprimes/programs/abundant_lucas-carmichael_cached.pl)
        * [almost-extra-strong-lucas not extra-strong-lucas.pl](./pseudoprimes/programs/almost-extra-strong-lucas_not_extra-strong-lucas.pl)
        * [almost abundant carmichael.pl](./pseudoprimes/programs/almost_abundant_carmichael.pl)
        * [almost carmichael pseudoprime.pl](./pseudoprimes/programs/almost_carmichael_pseudoprime.pl)
        * [almost carmichael pseudoprime cached.pl](./pseudoprimes/programs/almost_carmichael_pseudoprime_cached.pl)
        * [almost carmichael pseudoprime db.pl](./pseudoprimes/programs/almost_carmichael_pseudoprime_db.pl)
        * [antti lehmer problem.pl](./pseudoprimes/programs/antti_lehmer_problem.pl)
        * [antti lehmer problem smooth numbers.pl](./pseudoprimes/programs/antti_lehmer_problem_smooth_numbers.pl)
        * [benoit primes 1 cached.pl](./pseudoprimes/programs/benoit_primes_1_cached.pl)
        * [benoit primes 2 cached.pl](./pseudoprimes/programs/benoit_primes_2_cached.pl)
        * [bfw pseudoprime db.pl](./pseudoprimes/programs/bfw_pseudoprime_db.pl)
        * [binary period pseudoprimes.pl](./pseudoprimes/programs/binary_period_pseudoprimes.pl)
        * [binary search in file.pl](./pseudoprimes/programs/binary_search_in_file.pl)
        * [bpsw pseudoprime 1.pl](./pseudoprimes/programs/bpsw_pseudoprime_1.pl)
        * [bpsw pseudoprime 2.pl](./pseudoprimes/programs/bpsw_pseudoprime_2.pl)
        * [bpsw pseudoprime 3.pl](./pseudoprimes/programs/bpsw_pseudoprime_3.pl)
        * [bpsw pseudoprime 4.pl](./pseudoprimes/programs/bpsw_pseudoprime_4.pl)
        * [bpsw pseudoprime db.pl](./pseudoprimes/programs/bpsw_pseudoprime_db.pl)
        * [Cache](./pseudoprimes/programs/cache)
            * [cache.pl](./pseudoprimes/programs/cache/cache.pl)
            * [dbm2perl carmichael.pl](./pseudoprimes/programs/cache/dbm2perl_carmichael.pl)
            * [dbm2perl fermat.pl](./pseudoprimes/programs/cache/dbm2perl_fermat.pl)
            * [dbm2perl lucas-carmichael.pl](./pseudoprimes/programs/cache/dbm2perl_lucas-carmichael.pl)
            * [dbm2perl superpsp.pl](./pseudoprimes/programs/cache/dbm2perl_superpsp.pl)
            * [dbm snippet.pl](./pseudoprimes/programs/cache/dbm_snippet.pl)
            * [rebuild all.pl](./pseudoprimes/programs/cache/rebuild_all.pl)
            * [recover factordb.pl](./pseudoprimes/programs/cache/recover_factordb.pl)
            * [sanitize.pl](./pseudoprimes/programs/cache/sanitize.pl)
            * [storable snippet.pl](./pseudoprimes/programs/cache/storable_snippet.pl)
        * [carmichael-bernoulli kn numbers cached.pl](./pseudoprimes/programs/carmichael-bernoulli_kn_numbers_cached.pl)
        * [carmichael-bernoulli numbers cached.pl](./pseudoprimes/programs/carmichael-bernoulli_numbers_cached.pl)
        * [carmichael-lucas-carmichael from factors cached.pl](./pseudoprimes/programs/carmichael-lucas-carmichael_from_factors_cached.pl)
        * [carmichael divisible by 255 cached.pl](./pseudoprimes/programs/carmichael_divisible_by_255_cached.pl)
        * [carmichael from divisors.pl](./pseudoprimes/programs/carmichael_from_divisors.pl)
        * [carmichael from super psp cached.pl](./pseudoprimes/programs/carmichael_from_super_psp_cached.pl)
        * [carmichael gcd is carmichael cached.pl](./pseudoprimes/programs/carmichael_gcd_is_carmichael_cached.pl)
        * [carmichael gpf(p-1) = prime(n).pl](./pseudoprimes/programs/carmichael_gpf(p-1)%20=%20prime(n).pl)
        * [carmichael in range cached.pl](./pseudoprimes/programs/carmichael_in_range_cached.pl)
        * [carmichael is fibonacci cached.pl](./pseudoprimes/programs/carmichael_is_fibonacci_cached.pl)
        * [carmichael lambda.pl](./pseudoprimes/programs/carmichael_lambda.pl)
        * [carmichael lambda+1 is prime cached.pl](./pseudoprimes/programs/carmichael_lambda+1_is_prime_cached.pl)
        * [carmichael lambdas cached.pl](./pseudoprimes/programs/carmichael_lambdas_cached.pl)
        * [carmichael lcm factor is carmichael.pl](./pseudoprimes/programs/carmichael_lcm_factor_is_carmichael.pl)
        * [carmichael lcm is carmichael cached.pl](./pseudoprimes/programs/carmichael_lcm_is_carmichael_cached.pl)
        * [carmichael m-1 is power.pl](./pseudoprimes/programs/carmichael_m-1_is_power.pl)
        * [carmichael m-1 is power cached.pl](./pseudoprimes/programs/carmichael_m-1_is_power_cached.pl)
        * [carmichael m-1 is square.pl](./pseudoprimes/programs/carmichael_m-1_is_square.pl)
        * [carmichael multiples of cyclic numbers upper-bounds.pl](./pseudoprimes/programs/carmichael_multiples_of_cyclic_numbers_upper-bounds.pl)
        * [carmichael multiples of cyclic numbers upper-bounds cached.pl](./pseudoprimes/programs/carmichael_multiples_of_cyclic_numbers_upper-bounds_cached.pl)
        * [carmichael n-2 and n+2 are prime.pl](./pseudoprimes/programs/carmichael_n-2_and_n+2_are_prime.pl)
        * [carmichael of order 2.pl](./pseudoprimes/programs/carmichael_of_order_2.pl)
        * [carmichael of order 2 cached.pl](./pseudoprimes/programs/carmichael_of_order_2_cached.pl)
        * [carmichael of order 2 from factors cached.pl](./pseudoprimes/programs/carmichael_of_order_2_from_factors_cached.pl)
        * [carmichael of order 4 cached.pl](./pseudoprimes/programs/carmichael_of_order_4_cached.pl)
        * [carmichael overpseudoprimes cached.pl](./pseudoprimes/programs/carmichael_overpseudoprimes_cached.pl)
        * [carmichael p==3 mod 80.pl](./pseudoprimes/programs/carmichael_p==3_mod_80.pl)
        * [carmichael p==3 mod 80 cached.pl](./pseudoprimes/programs/carmichael_p==3_mod_80_cached.pl)
        * [carmichael phi-lambda conjecture cached.pl](./pseudoprimes/programs/carmichael_phi-lambda_conjecture_cached.pl)
        * [carmichael rad(p-1)==rad(n-1) cached.pl](./pseudoprimes/programs/carmichael_rad(p-1)==rad(n-1)_cached.pl)
        * [carmichael rad(p-1)==rad(n-1) db.pl](./pseudoprimes/programs/carmichael_rad(p-1)==rad(n-1)_db.pl)
        * [carmichael strong psp with n factors cached.pl](./pseudoprimes/programs/carmichael_strong_psp_with_n_factors_cached.pl)
        * [carmichael superpseudoprimes.pl](./pseudoprimes/programs/carmichael_superpseudoprimes.pl)
        * [carmichael superpseudoprimes cached.pl](./pseudoprimes/programs/carmichael_superpseudoprimes_cached.pl)
        * [carmichael where gpf(n)+1|n+1.pl](./pseudoprimes/programs/carmichael_where_gpf(n)+1|n+1.pl)
        * [carmichael where gpf(n)+1|n+1 cached.pl](./pseudoprimes/programs/carmichael_where_gpf(n)+1|n+1_cached.pl)
        * [carmichael where p+1|n+1.pl](./pseudoprimes/programs/carmichael_where_p+1|n+1.pl)
        * [carmichael where phi(k) does not divide (k-1)^n cached.pl](./pseudoprimes/programs/carmichael_where_phi(k)_does_not_divide_(k-1)^n_cached.pl)
        * [carmichael with 3 factors p+1|n+1.pl](./pseudoprimes/programs/carmichael_with_3_factors_p+1|n+1.pl)
        * [carmichael with 3 factors p+1|n+1 cached.pl](./pseudoprimes/programs/carmichael_with_3_factors_p+1|n+1_cached.pl)
        * [carmichael with consecutive factors cached.pl](./pseudoprimes/programs/carmichael_with_consecutive_factors_cached.pl)
        * [carmichael with gcd phi lambda cached.pl](./pseudoprimes/programs/carmichael_with_gcd_phi_lambda_cached.pl)
        * [carmichael with large lehmer index cached.pl](./pseudoprimes/programs/carmichael_with_large_lehmer_index_cached.pl)
        * [carmichael with only odd digits cached.pl](./pseudoprimes/programs/carmichael_with_only_odd_digits_cached.pl)
        * [central polygonal carmichael.pl](./pseudoprimes/programs/central_polygonal_carmichael.pl)
        * [chebyshev pseudoprimes.pl](./pseudoprimes/programs/chebyshev_pseudoprimes.pl)
        * [consecutive fermat.pl](./pseudoprimes/programs/consecutive_fermat.pl)
        * [consecutive fermat below 2^64.pl](./pseudoprimes/programs/consecutive_fermat_below_2^64.pl)
        * [eldar carmichael numbers cached.pl](./pseudoprimes/programs/eldar_carmichael_numbers_cached.pl)
        * [emirp carmichael cached.pl](./pseudoprimes/programs/emirp_carmichael_cached.pl)
        * [euler jacobi psp to first n bases db.pl](./pseudoprimes/programs/euler_jacobi_psp_to_first_n_bases_db.pl)
        * [euler jacobi psp to first n bases txt.pl](./pseudoprimes/programs/euler_jacobi_psp_to_first_n_bases_txt.pl)
        * [euler trinomial strong psp.pl](./pseudoprimes/programs/euler_trinomial_strong_psp.pl)
        * [extra-strong lucas not lucas.pl](./pseudoprimes/programs/extra-strong_lucas_not_lucas.pl)
        * [factorize pseudoprime.pl](./pseudoprimes/programs/factorize_pseudoprime.pl)
        * [factorize pseudoprimes.pl](./pseudoprimes/programs/factorize_pseudoprimes.pl)
        * [factors of 2^n-1 overpseudoprimes.pl](./pseudoprimes/programs/factors_of_2^n-1_overpseudoprimes.pl)
        * [factors of 2^n-1 psp.pl](./pseudoprimes/programs/factors_of_2^n-1_psp.pl)
        * [factors of 2^n-1 strong psp.pl](./pseudoprimes/programs/factors_of_2^n-1_strong_psp.pl)
        * [factors of mersenne.pl](./pseudoprimes/programs/factors_of_mersenne.pl)
        * [fermat3 m-1 is square.pl](./pseudoprimes/programs/fermat3_m-1_is_square.pl)
        * [fermat 2^n == 2 (mod n*(n-1)).pl](./pseudoprimes/programs/fermat_2^n%20==%202%20(mod%20n*(n-1)).pl)
        * [fermat 2n+1 is pseudoprime.pl](./pseudoprimes/programs/fermat_2n+1_is_pseudoprime.pl)
        * [fermat base n with n factors.pl](./pseudoprimes/programs/fermat_base_n_with_n_factors.pl)
        * [fermat from divisors.pl](./pseudoprimes/programs/fermat_from_divisors.pl)
        * [fermat from fermat cached.pl](./pseudoprimes/programs/fermat_from_fermat_cached.pl)
        * [fermat gpf(p-1) = prime(n).pl](./pseudoprimes/programs/fermat_gpf(p-1)%20=%20prime(n).pl)
        * [fermat m-1 is cube.pl](./pseudoprimes/programs/fermat_m-1_is_cube.pl)
        * [fermat p==3 mod 80.pl](./pseudoprimes/programs/fermat_p==3_mod_80.pl)
        * [fermat p==3 mod 80 bellow 2^64.pl](./pseudoprimes/programs/fermat_p==3_mod_80_bellow_2^64.pl)
        * [fermat p==3 mod 80 cached.pl](./pseudoprimes/programs/fermat_p==3_mod_80_cached.pl)
        * [fermat p==3 mod 80 db.pl](./pseudoprimes/programs/fermat_p==3_mod_80_db.pl)
        * [fermat psp with n factors db.pl](./pseudoprimes/programs/fermat_psp_with_n_factors_db.pl)
        * [fermat with large lehmer index cached.pl](./pseudoprimes/programs/fermat_with_large_lehmer_index_cached.pl)
        * [fermat with n factors where p-1 does not divide k-1.pl](./pseudoprimes/programs/fermat_with_n_factors_where_p-1_does_not_divide_k-1.pl)
        * [fermat with n factors where p-1 does not divide k-1 cached.pl](./pseudoprimes/programs/fermat_with_n_factors_where_p-1_does_not_divide_k-1_cached.pl)
        * [fermat with n factors where p-1 does not divide k-1 db.pl](./pseudoprimes/programs/fermat_with_n_factors_where_p-1_does_not_divide_k-1_db.pl)
        * [fib n and n+1 divides sum of fib.pl](./pseudoprimes/programs/fib_n_and_n+1_divides_sum_of_fib.pl)
        * [five consecutive odd pseudoprimes.pl](./pseudoprimes/programs/five_consecutive_odd_pseudoprimes.pl)
        * [frobenius pseudoprime.pl](./pseudoprimes/programs/frobenius_pseudoprime.pl)
        * [gauss-euler counterexample.pl](./pseudoprimes/programs/gauss-euler_counterexample.pl)
        * [gauss-euler counterexample db.pl](./pseudoprimes/programs/gauss-euler_counterexample_db.pl)
        * [generate carmichael with p==q mod 12 comb db.pl](./pseudoprimes/programs/generate_carmichael_with_p==q_mod_12_comb_db.pl)
        * [generate carmichael with p==q mod 12 db.pl](./pseudoprimes/programs/generate_carmichael_with_p==q_mod_12_db.pl)
        * [generate pseudoprimes from factors.pl](./pseudoprimes/programs/generate_pseudoprimes_from_factors.pl)
        * [generate pseudoprimes from factors cached.pl](./pseudoprimes/programs/generate_pseudoprimes_from_factors_cached.pl)
        * [generate psp from prime factors db.pl](./pseudoprimes/programs/generate_psp_from_prime_factors_db.pl)
        * [generate psp from psp db.pl](./pseudoprimes/programs/generate_psp_from_psp_db.pl)
        * [giuga conjecture.pl](./pseudoprimes/programs/giuga_conjecture.pl)
        * [giuga conjecture cached.pl](./pseudoprimes/programs/giuga_conjecture_cached.pl)
        * [imprimitive carmichael with n factors.pl](./pseudoprimes/programs/imprimitive_carmichael_with_n_factors.pl)
        * [imprimitive carmichael with n factors cached.pl](./pseudoprimes/programs/imprimitive_carmichael_with_n_factors_cached.pl)
        * [is bpsw pseudoprime.pl](./pseudoprimes/programs/is_bpsw_pseudoprime.pl)
        * [is euler-fibonacci pseudoprime.pl](./pseudoprimes/programs/is_euler-fibonacci_pseudoprime.pl)
        * [is frobenius khashin pseudoprime.pl](./pseudoprimes/programs/is_frobenius_khashin_pseudoprime.pl)
        * [is frobenius pseudoprime.pl](./pseudoprimes/programs/is_frobenius_pseudoprime.pl)
        * [is frobenius underwood pseudoprime.pl](./pseudoprimes/programs/is_frobenius_underwood_pseudoprime.pl)
        * [is mpz pseudoprime.pl](./pseudoprimes/programs/is_mpz_pseudoprime.pl)
        * [is perrin pseudoprime.pl](./pseudoprimes/programs/is_perrin_pseudoprime.pl)
        * [is quadratic frobenius pseudoprime.pl](./pseudoprimes/programs/is_quadratic_frobenius_pseudoprime.pl)
        * [janfeitsma contains check.pl](./pseudoprimes/programs/janfeitsma_contains_check.pl)
        * [lambda carmichael numbers cached.pl](./pseudoprimes/programs/lambda_carmichael_numbers_cached.pl)
        * [largest ndigit carmichael.pl](./pseudoprimes/programs/largest_ndigit_carmichael.pl)
        * [largest ndigit carmichael cached.pl](./pseudoprimes/programs/largest_ndigit_carmichael_cached.pl)
        * [largest ndigit pseudoprime.pl](./pseudoprimes/programs/largest_ndigit_pseudoprime.pl)
        * [largest ndigit pseudoprime cached.pl](./pseudoprimes/programs/largest_ndigit_pseudoprime_cached.pl)
        * [lehmer totient conjecture.pl](./pseudoprimes/programs/lehmer_totient_conjecture.pl)
        * [lehmer totient conjecture cached.pl](./pseudoprimes/programs/lehmer_totient_conjecture_cached.pl)
        * [lehmer totient weak numbers cached.pl](./pseudoprimes/programs/lehmer_totient_weak_numbers_cached.pl)
        * [lehmer totient weak numbers native.pl](./pseudoprimes/programs/lehmer_totient_weak_numbers_native.pl)
        * [lucas(n)==2 mod n.pl](./pseudoprimes/programs/lucas(n)==2_mod_n.pl)
        * [lucas-carmichael-fermat pseudoprime cached.pl](./pseudoprimes/programs/lucas-carmichael-fermat_pseudoprime_cached.pl)
        * [lucas-carmichael conjecture.pl](./pseudoprimes/programs/lucas-carmichael_conjecture.pl)
        * [lucas-carmichael conjecture cached.pl](./pseudoprimes/programs/lucas-carmichael_conjecture_cached.pl)
        * [lucas-carmichael gcd is term cached.pl](./pseudoprimes/programs/lucas-carmichael_gcd_is_term_cached.pl)
        * [lucas-carmichael lambda+1 is prime cached.pl](./pseudoprimes/programs/lucas-carmichael_lambda+1_is_prime_cached.pl)
        * [lucas-carmichael lambdas cached.pl](./pseudoprimes/programs/lucas-carmichael_lambdas_cached.pl)
        * [lucas-carmichael lcm is term cached.pl](./pseudoprimes/programs/lucas-carmichael_lcm_is_term_cached.pl)
        * [lucas-carmichael multiples of lucas-cyclic numbers.pl](./pseudoprimes/programs/lucas-carmichael_multiples_of_lucas-cyclic_numbers.pl)
        * [lucas-carmichael multiples of lucas-cyclic numbers cached.pl](./pseudoprimes/programs/lucas-carmichael_multiples_of_lucas-cyclic_numbers_cached.pl)
        * [lucas-carmichael plus 1 divides sigma(n).pl](./pseudoprimes/programs/lucas-carmichael_plus_1_divides_sigma(n).pl)
        * [lucas-carmichael where gpf(n)-1|n-1 cached.pl](./pseudoprimes/programs/lucas-carmichael_where_gpf(n)-1|n-1_cached.pl)
        * [lucas-carmichael with 3 factors p-1|n-1.pl](./pseudoprimes/programs/lucas-carmichael_with_3_factors_p-1|n-1.pl)
        * [lucas-carmichael with 3 factors p-1|n-1 cached.pl](./pseudoprimes/programs/lucas-carmichael_with_3_factors_p-1|n-1_cached.pl)
        * [lucas-carmichael with large lehmer index cached.pl](./pseudoprimes/programs/lucas-carmichael_with_large_lehmer_index_cached.pl)
        * [lucas-carmichael with n factors.pl](./pseudoprimes/programs/lucas-carmichael_with_n_factors.pl)
        * [lucas-carmichael with n factors cached.pl](./pseudoprimes/programs/lucas-carmichael_with_n_factors_cached.pl)
        * [lucas-fermat conjecture cached.pl](./pseudoprimes/programs/lucas-fermat_conjecture_cached.pl)
        * [lucas-fermat pseudoprime.pl](./pseudoprimes/programs/lucas-fermat_pseudoprime.pl)
        * [lucas restricted domain primality test.sf](./pseudoprimes/programs/lucas_restricted_domain_primality_test.sf)
        * [lucas V pseudoprimes.pl](./pseudoprimes/programs/lucas_V_pseudoprimes.pl)
        * [n+1 divides sigma(n) db.pl](./pseudoprimes/programs/n+1_divides_sigma(n)_db.pl)
        * [new psp2.pl](./pseudoprimes/programs/new_psp2.pl)
        * [nine nine nine pseudoprimes.pl](./pseudoprimes/programs/nine_nine_nine_pseudoprimes.pl)
        * [non-pandigital carmichael cached.pl](./pseudoprimes/programs/non-pandigital_carmichael_cached.pl)
        * [non-residue fermat records.pl](./pseudoprimes/programs/non-residue_fermat_records.pl)
        * [non-residue fermat records below 2^64.pl](./pseudoprimes/programs/non-residue_fermat_records_below_2^64.pl)
        * [non-residue pseudoprimes.pl](./pseudoprimes/programs/non-residue_pseudoprimes.pl)
        * [non-residue pseudoprimes below 2^64.pl](./pseudoprimes/programs/non-residue_pseudoprimes_below_2^64.pl)
        * [nonsquarefree pseudoprimes.pl](./pseudoprimes/programs/nonsquarefree_pseudoprimes.pl)
        * [odd part of carmichael-1 is carmichael.pl](./pseudoprimes/programs/odd_part_of_carmichael-1_is_carmichael.pl)
        * [Other](./pseudoprimes/programs/other)
            * [batch gcd factorization.sf](./pseudoprimes/programs/other/batch_gcd_factorization.sf)
            * [BPSW primality test.pl](./pseudoprimes/programs/other/BPSW_primality_test.pl)
            * [BPSW primality test anynum.pl](./pseudoprimes/programs/other/BPSW_primality_test_anynum.pl)
            * [BPSW primality test mpz.pl](./pseudoprimes/programs/other/BPSW_primality_test_mpz.pl)
            * [check factordb.sf](./pseudoprimes/programs/other/check_factordb.sf)
            * [fib-tzn primality test.pl](./pseudoprimes/programs/other/fib-tzn_primality_test.pl)
            * [fib-tzn primality test.sf](./pseudoprimes/programs/other/fib-tzn_primality_test.sf)
            * [fib-tzn strong primality test.pl](./pseudoprimes/programs/other/fib-tzn_strong_primality_test.pl)
            * [find bfw psp.sf](./pseudoprimes/programs/other/find_bfw_psp.sf)
            * [math-anynum.pl](./pseudoprimes/programs/other/math-anynum.pl)
            * [pseudoprime factorization.sf](./pseudoprimes/programs/other/pseudoprime_factorization.sf)
            * [PSW primality test.pl](./pseudoprimes/programs/other/PSW_primality_test.pl)
            * [PSW primality test ntheory.pl](./pseudoprimes/programs/other/PSW_primality_test_ntheory.pl)
            * [test.pl](./pseudoprimes/programs/other/test.pl)
            * [test2.pl](./pseudoprimes/programs/other/test2.pl)
            * [test3.pl](./pseudoprimes/programs/other/test3.pl)
            * [test fermat fib.pl](./pseudoprimes/programs/other/test_fermat_fib.pl)
            * [test fib-tzn.pl](./pseudoprimes/programs/other/test_fib-tzn.pl)
            * [test fib prime.pl](./pseudoprimes/programs/other/test_fib_prime.pl)
        * [overpseudoprimes with n factors cached.pl](./pseudoprimes/programs/overpseudoprimes_with_n_factors_cached.pl)
        * [palindromic fibonacci.pl](./pseudoprimes/programs/palindromic_fibonacci.pl)
        * [palindromic lucas.pl](./pseudoprimes/programs/palindromic_lucas.pl)
        * [palindromic pseudoprimes.pl](./pseudoprimes/programs/palindromic_pseudoprimes.pl)
        * [palindromic pseudoprimes in base n.pl](./pseudoprimes/programs/palindromic_pseudoprimes_in_base_n.pl)
        * [phi(k) divides k-3.pl](./pseudoprimes/programs/phi(k)_divides_k-3.pl)
        * [phi(n) divides n+1 db.pl](./pseudoprimes/programs/phi(n)_divides_n+1_db.pl)
        * [pomerance fib test.pl](./pseudoprimes/programs/pomerance_fib_test.pl)
        * [pomerance smooth primes cached.pl](./pseudoprimes/programs/pomerance_smooth_primes_cached.pl)
        * [pomerance smooth primes from factors.pl](./pseudoprimes/programs/pomerance_smooth_primes_from_factors.pl)
        * [primary carmichael with n prime factors cached.pl](./pseudoprimes/programs/primary_carmichael_with_n_prime_factors_cached.pl)
        * [prime gaps db.pl](./pseudoprimes/programs/prime_gaps_db.pl)
        * [pseudoprime surrounded by primes.pl](./pseudoprimes/programs/pseudoprime_surrounded_by_primes.pl)
        * [pseudoprimes of the form 6p+1.pl](./pseudoprimes/programs/pseudoprimes_of_the_form_6p+1.pl)
        * [pseudoprimes with only odd digits.pl](./pseudoprimes/programs/pseudoprimes_with_only_odd_digits.pl)
        * [reversible lucas.pl](./pseudoprimes/programs/reversible_lucas.pl)
        * [reversible pseudoprimes.pl](./pseudoprimes/programs/reversible_pseudoprimes.pl)
        * [safe pseudoprimes.pl](./pseudoprimes/programs/safe_pseudoprimes.pl)
        * [similar lehmer totient weak numbers native.pl](./pseudoprimes/programs/similar_lehmer_totient_weak_numbers_native.pl)
        * [smallest carmichael-kronecker with n factors cached.pl](./pseudoprimes/programs/smallest_carmichael-kronecker_with_n_factors_cached.pl)
        * [smallest carmichael with n factors.pl](./pseudoprimes/programs/smallest_carmichael_with_n_factors.pl)
        * [smallest carmichael with n factors cached.pl](./pseudoprimes/programs/smallest_carmichael_with_n_factors_cached.pl)
        * [smallest fermat with n factors.pl](./pseudoprimes/programs/smallest_fermat_with_n_factors.pl)
        * [smallest fermat with n factors cached.pl](./pseudoprimes/programs/smallest_fermat_with_n_factors_cached.pl)
        * [smallest fibonacci psp with n factors.pl](./pseudoprimes/programs/smallest_fibonacci_psp_with_n_factors.pl)
        * [smallest k such that p^k==p (mod k).pl](./pseudoprimes/programs/smallest_k_such_that_p^k==p_(mod%20k).pl)
        * [smallest ndigit carmichael.pl](./pseudoprimes/programs/smallest_ndigit_carmichael.pl)
        * [smallest ndigit carmichael cached.pl](./pseudoprimes/programs/smallest_ndigit_carmichael_cached.pl)
        * [smallest ndigit pseudoprime.pl](./pseudoprimes/programs/smallest_ndigit_pseudoprime.pl)
        * [smallest ndigit pseudoprime cached.pl](./pseudoprimes/programs/smallest_ndigit_pseudoprime_cached.pl)
        * [smallest strong pseudoprime to the first n bases cached.pl](./pseudoprimes/programs/smallest_strong_pseudoprime_to_the_first_n_bases_cached.pl)
        * [smallest strong pseudoprime to the first n prime bases cached.pl](./pseudoprimes/programs/smallest_strong_pseudoprime_to_the_first_n_prime_bases_cached.pl)
        * [smallest superpseudoprime to the first n bases cached.pl](./pseudoprimes/programs/smallest_superpseudoprime_to_the_first_n_bases_cached.pl)
        * [smooth primes.pl](./pseudoprimes/programs/smooth_primes.pl)
        * [smooth primes 2.pl](./pseudoprimes/programs/smooth_primes_2.pl)
        * [solovay strassen pseudoprimes.pl](./pseudoprimes/programs/solovay_strassen_pseudoprimes.pl)
        * [steuerwald-ordowsk theorem.pl](./pseudoprimes/programs/steuerwald-ordowsk_theorem.pl)
        * [strong miller rabin pseudoprimes.pl](./pseudoprimes/programs/strong_miller_rabin_pseudoprimes.pl)
        * [strong miller rabin pseudoprimes cached.pl](./pseudoprimes/programs/strong_miller_rabin_pseudoprimes_cached.pl)
        * [strong psp n-2 and n+2 are prime.pl](./pseudoprimes/programs/strong_psp_n-2_and_n+2_are_prime.pl)
        * [strong psp with n prime factors.pl](./pseudoprimes/programs/strong_psp_with_n_prime_factors.pl)
        * [super-poulet with n factors.pl](./pseudoprimes/programs/super-poulet_with_n_factors.pl)
        * [super-poulet with n factors cached.pl](./pseudoprimes/programs/super-poulet_with_n_factors_cached.pl)
        * [super primitive primes.pl](./pseudoprimes/programs/super_primitive_primes.pl)
        * [superpseudoprimes.pl](./pseudoprimes/programs/superpseudoprimes.pl)
        * [superpseudoprimes cached.pl](./pseudoprimes/programs/superpseudoprimes_cached.pl)
        * [tomasz A309284 db.pl](./pseudoprimes/programs/tomasz_A309284_db.pl)
        * [tomasz A309285 db.pl](./pseudoprimes/programs/tomasz_A309285_db.pl)
        * [tomasz pseudoprimes cached.pl](./pseudoprimes/programs/tomasz_pseudoprimes_cached.pl)
        * [twin lucas.pl](./pseudoprimes/programs/twin_lucas.pl)
        * [twin pseudoprimes.pl](./pseudoprimes/programs/twin_pseudoprimes.pl)
        * [very strong lucas.pl](./pseudoprimes/programs/very_strong_lucas.pl)
        * [wall-sun-sun primes cached.pl](./pseudoprimes/programs/wall-sun-sun_primes_cached.pl)
        * [weak lucas.pl](./pseudoprimes/programs/weak_lucas.pl)
        * [wieferich primes.pl](./pseudoprimes/programs/wieferich_primes.pl)
        * [wieferich primes cached.pl](./pseudoprimes/programs/wieferich_primes_cached.pl)
        * [wilson primes cached.pl](./pseudoprimes/programs/wilson_primes_cached.pl)
    * [Util](./pseudoprimes/util)
        * [carmichael.pl](./pseudoprimes/util/carmichael.pl)
        * [deduplicate.pl](./pseudoprimes/util/deduplicate.pl)
        * [group.pl](./pseudoprimes/util/group.pl)
        * [group pseudoprimes.sf](./pseudoprimes/util/group_pseudoprimes.sf)
        * [group pseudoprimes 2.sf](./pseudoprimes/util/group_pseudoprimes_2.sf)
        * [psp with large gpf.pl](./pseudoprimes/util/psp_with_large_gpf.pl)
        * [separate carmichael.pl](./pseudoprimes/util/separate_carmichael.pl)
        * [sort carmichael.pl](./pseudoprimes/util/sort_carmichael.pl)
        * [super psp.pl](./pseudoprimes/util/super_psp.pl)
        * [uniq file.pl](./pseudoprimes/util/uniq_file.pl)
        * [zsort.pl](./pseudoprimes/util/zsort.pl)
    * [verify new carmichael.pl](./pseudoprimes/verify_new_carmichael.pl)
* [Sloane-gap](./sloane-gap)
    * [extract.pl](./sloane-gap/extract.pl)
    * [generate.pl](./sloane-gap/generate.pl)

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