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 A372943 #9 May 18 2024 01:49:40
%S A372943 1,3,21,147,217,781,903,1323,3249,3267,3591,5929,6897,7623,8001,8673,
%T A372943 10017,11187,11997,17181,21413,21791,23529,38829,51183,54033,58653,
%U A372943 68229,71391,75593,83853,87813,97641,128331,171647,217143,227829,249159,302841,307347,389403
%N A372943 Numbers k that divide the k-th Apéry number (A005258).
%C A372943 Numbers k such that k | A005258(k).
%H A372943 Amiram Eldar, <a href="/A372943/b372943.txt">Table of n, a(n) for n = 1..143</a>
%e A372943 3 is a term since A005258(3) = 147 = 3 * 49 is divisible by 3.
%t A372943 seq[kmax_] := Module[{ap0 = 1, ap1 = 3, ap2, s = {1}}, Do[ap2 = ((11*k^2 - 11*k + 3)*ap1 + (k-1)^2*ap0)/k^2; If[Divisible[ap2, k], AppendTo[s, k]]; ap0 = ap1; ap1 = ap2, {k, 2, kmax}]; s]; seq[5000]
%o A372943 (PARI) lista(kmax) = {my(ap0 = 1, ap1 = 3, ap2); print1("1, "); for(k = 2, kmax, ap2 = ((11*k^2 - 11*k + 3)*ap1 + (k-1)^2*ap0)/k^2; if(!(ap2 % k), print1(k, ", ")); ap0 = ap1; ap1 = ap2);}
%Y A372943 Cf. A005258.
%Y A372943 Similar sequences: A014847 (Catalan), A016089 (Lucas), A023172 (Fibonacci), A051177 (partition), A232570 (tribonacci), A246692 (Pell), A266969 (Motzkin).
%K A372943 nonn
%O A372943 1,2
%A A372943 _Amiram Eldar_, May 17 2024