A372943 Numbers k that divide the k-th Apéry number (A005258).

1, 3, 21, 147, 217, 781, 903, 1323, 3249, 3267, 3591, 5929, 6897, 7623, 8001, 8673, 10017, 11187, 11997, 17181, 21413, 21791, 23529, 38829, 51183, 54033, 58653, 68229, 71391, 75593, 83853, 87813, 97641, 128331, 171647, 217143, 227829, 249159, 302841, 307347, 389403

Offset: 1

Author

Amiram Eldar, May 17 2024

Keywords

• nonn

Comments

Numbers k such that k | A005258(k).

Examples

			3 is a term since A005258(3) = 147 = 3 * 49 is divisible by 3.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..143

Crossrefs

Cf. A005258.

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

Programs

Mathematica

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]

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);}