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 A131191 #7 Feb 02 2015 21:42:19 %S A131191 7,18,29,40,51,62,73,84,95,106,128,139,150,161,172,183,194,205,216, %T A131191 227,249,260,271,282,293,304,315,326,337,348,370,381,392,403,414,425, %U A131191 436,447,458,469,491,502,513,524,535,546,557,568,579,590,612,623,634,645,656,667,678,689,700,711,733,744 %N A131191 Numbers n>=0 such that d(n) = (n^1 + 1) (n^2 + 2) ... (n^22 + 22) / 22!, e(n) = (n^1 + 1) (n^2 + 2) ... (n^23 + 23) / 23!, and f(n) = (n^1 + 1) (n^2 + 2) ... (n^24 + 24) / 24! take nonintegral values. %C A131191 If n is in this sequence, then so is n+121. - _Max Alekseyev_, Feb 02 2015 %F A131191 Notice that 22! = 2^19 * 3^9 * 5^4 * 7^3 * 11^2 * 13 * 17 * 19. All these prime powers divide (n^1 + 1)*(n^2 + 2)*(n^3 +3)*...*(n^22 + 22), except for 11^2. 11^2 does not divide (n^1 + 1)*(n^2 + 2)*(n^3 + 3)*...*(n^22 + 22) for n = 7, 18, 29, 40, 51, 62, 73, 84, 95, 106 modulo 121. That is, d(n) is nonintegral for n the form 11m+7 but not 121m+117, and so are e(n) and f(n). - _Max Alekseyev_, Nov 10 2007 %Y A131191 Cf. A017473, A129995 %K A131191 nonn %O A131191 1,1 %A A131191 _Alexander R. Povolotsky_, Sep 25 2007 %E A131191 Initial terms were calculated by Peter J. C. Moses; see comment in A129995. %E A131191 More terms from _Max Alekseyev_, Feb 02 2015