This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A116912 #14 Jan 10 2020 06:16:30 %S A116912 1,2,3,4,1,6,11,8,9,2,7,12,17,22,3,16,13,18,23,4,33,14,19,24,1,34,27, %T A116912 44,25,6,35,32,21,26,11,36,41,46,51,8,37,66,47,28,9,38,43,48,121,2,39, %U A116912 68,49,54,7,88,69,50,55,12,65,70,99,64 %N A116912 In prime factorization of n replace all primes of form k*6+1 with k*6+5 and primes of form k*6+5 with k*6+1. %C A116912 Primes of form 6n + 1 are also primes of the form 3n+1 and -3 is a quadratic residue mod a prime p iff p is in this sequence. Primes of the form 6n + 5 are the same as A003627 Primes of form 3n-1, except that the latter sequence starts with 2. Every twin prime after (3,5) is of the form (6n+5, 6n+1) hence the current sequence exchanges lesser twin primes with greater twin primes. See also: A072010 In prime factorization of n replace all primes of form k*4+1 by k*4+3 and primes of form k*4+3 by k*4+1. See also: A002476 Primes of form 6n + 1. %H A116912 Amiram Eldar, <a href="/A116912/b116912.txt">Table of n, a(n) for n = 1..10000</a> %F A116912 Multiplicative. a(2^n) = 2^n, a(3^n) = 3^n, a(5^n) = 1, a(7^n) = 11^n, a(11^n) = 7^n, a(13^n) = 17^n, a(17^n) = 13^n, a(19^n) = 23^n, a(23^n) = 19^n, a(29^n) = 5^(2n), a(31^n) = (5^n)*(7^n), a(37^n) = 41^n, a(41^n) = 37^n, a(43^n) = 47^n, a(47^n) = 43^n, a(53^n) = 7^(2n), a(59^n) = (5^n)*(11^n), a(61^n) = (5^n)*(13^n), ... %e A116912 a(5) = 1 because 5 is a prime of the form 6n + 5 (with n = 0), so is replaced with 6n + 1 (with n = 0), namely 1. %e A116912 a(7) = 11 because 7 is a prime of the form 6n + 1 (with n = 1), so is replaced with 6n + 5 (with n = 1), namely 11. %e A116912 a(11) = 7 because 11 is a prime of the form 6n + 5 (with n = 1), so is replaced with 6n + 1 (with n = 1), namely 7. %e A116912 a(13) = 17 because 13 is a prime of the form 6n + 1 (with n = 2), so is replaced with 6n + 5 (with n = 2), namely 17. %e A116912 a(14) = 22 because 14 = 2 * 7; but 7 is a prime of the form 6n + 1 (with n = 1), so is replaced with 6n + 5 (with n = 1), namely 11; giving 2 * 11 = 22. %t A116912 f[p_, e_] := If[p < 5, p^e, (p + 6 - 2 * Mod[p, 6])^e]; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 64] (* _Amiram Eldar_, Jan 10 2020 *) %Y A116912 Cf. A002476, A003627, A072010. %K A116912 easy,nonn %O A116912 1,2 %A A116912 _Jonathan Vos Post_, Mar 18 2006 %E A116912 Data corrected by _Amiram Eldar_, Jan 10 2020