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 A113508 #26 Jun 02 2025 19:28:38
%S A113508 1,2,3,4,6,7,8,9,11,13,14,16,17,18,19,21,23,26,27,28,29,31,32,33,34,
%T A113508 37,38,39,41,42,43,46,47,49,52,53,54,56,57,58,59,61,62,63,64,67,68,69,
%U A113508 71,73,74,76,77,78,79,81,82,83,86,87,89,91,93,94,97,98,99,101
%N A113508 Pentagon-free numbers: numbers k such that no divisor of k is a pentagonal number > 1.
%C A113508 Pentagonal number analogy of A112886 (the triangle-free positive integers).
%C A113508 Density is empirically close to 12/(Pi^(5/2)). - _Richard Peterson_, Apr 06 2025
%H A113508 G. C. Greubel, <a href="/A113508/b113508.txt">Table of n, a(n) for n = 1..5000</a>
%e A113508 10 is not a term, since 10 = 2 * 5 and 5 is the first nontrivial pentagonal number.
%t A113508 Select[Range[1, 101], {} == Intersection[{5, 12, 22, 35, 51, 70, 92}, Divisors[#]] &] (* _Giovanni Resta_, Jun 13 2016 *)
%o A113508 (PARI) is(n)=fordiv(n, d, if(ispolygonal(d, 5) && d>1, return(0))); 1 \\ _Charles R Greathouse IV_, Dec 24 2018
%Y A113508 Cf. A000326, A112886, A113502.
%K A113508 easy,nonn
%O A113508 1,2
%A A113508 _Jonathan Vos Post_, Jan 11 2006
%E A113508 Data corrected by _Giovanni Resta_, Jun 13 2016
%E A113508 a(1)=1 inserted by _Andrew Howroyd_, Sep 08 2024