A372942 Numbers k that divide the k-th Apéry number (A005259).

1, 5, 55, 629, 3439, 8525, 17629, 74455, 120275, 176305, 244915, 250325, 628975, 817819, 839135, 910675, 912865, 936955, 1118435, 1147925, 2344127, 4434125, 7795715, 7888477, 9276275, 10205525

Offset: 1

Author

Amiram Eldar, May 17 2024

Keywords

• nonn
• more

Comments

Numbers k such that k | A005259(k).

Crossrefs

Cf. A005259.

Similar sequences: A014847 (Catalan), A016089 (Lucas), A023172 (Fibonacci), A051177 (partition), A232570 (tribonacci), A246692 (Pell), A266969 (Motzkin).

Programs

Mathematica

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]

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);}

Formula

5 is a term since A005259(5) = 819005 = 5 * 163801 is divisible by 5.