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 A372942 #7 May 18 2024 01:49:44
%S A372942 1,5,55,629,3439,8525,17629,74455,120275,176305,244915,250325,628975,
%T A372942 817819,839135,910675,912865,936955,1118435,1147925,2344127,4434125,
%U A372942 7795715,7888477,9276275,10205525
%N A372942 Numbers k that divide the k-th Apéry number (A005259).
%C A372942 Numbers k such that k | A005259(k).
%F A372942 5 is a term since A005259(5) = 819005 = 5 * 163801 is divisible by 5.
%t A372942 seq[kmax_] := Module[{ap0 = 1, ap1 = 5, ap2, s = {1}}, Do[ap2 = ((34*k^3 - 51*k^2 + 27*k - 5)*ap1 - (k-1)^3*ap0)/k^3; If[Divisible[ap2, k], AppendTo[s, k]]; ap0 = ap1; ap1 = ap2, {k, 2, kmax}]; s]; seq[5000]
%o A372942 (PARI) lista(kmax) = {my(ap0 = 1, ap1 = 5, ap2); print1("1, "); for(k = 2, kmax, ap2 = ((34*k^3 - 51*k^2 + 27*k - 5)*ap1 - (k-1)^3*ap0)/k^3; if(!(ap2 % k), print1(k, ", ")); ap0 = ap1; ap1 = ap2);}
%Y A372942 Cf. A005259.
%Y A372942 Similar sequences: A014847 (Catalan), A016089 (Lucas), A023172 (Fibonacci), A051177 (partition), A232570 (tribonacci), A246692 (Pell), A266969 (Motzkin).
%K A372942 nonn,more
%O A372942 1,2
%A A372942 _Amiram Eldar_, May 17 2024