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A372943
Numbers k that divide the k-th Apéry number (A005258).
1
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
1,2
COMMENTS
Numbers k such that k | A005258(k).
LINKS
EXAMPLE
3 is a term since A005258(3) = 147 = 3 * 49 is divisible by 3.
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]
PROG
(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); }
CROSSREFS
Cf. A005258.
Similar sequences: A014847 (Catalan), A016089 (Lucas), A023172 (Fibonacci), A051177 (partition), A232570 (tribonacci), A246692 (Pell), A266969 (Motzkin).
Sequence in context: A243397 A173350 A323203 * A169634 A088088 A206638
KEYWORD
nonn
AUTHOR
Amiram Eldar, May 17 2024
STATUS
approved