A345465 a(n) = Sum_{d|n} (d!)^d.

1, 5, 217, 331781, 24883200001, 139314069504000221, 82606411253903523840000001, 6984964247141514123629140377600331781, 109110688415571316480344899355894085582848000000217, 395940866122425193243875570782668457763038822400000000024883200005

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..30

Formula

G.f.: Sum_{k >= 1} (k! * x)^k/(1 - x^k).

If p is prime, a(p) = 1 + (p!)^p.

Mathematica

Total/@Table[((Divisors[n])!)^Divisors[n], {n, 10}] (* Harvey P. Dale, Apr 24 2022 *)

Prog

(PARI) a(n) = sumdiv(n, d, d!^d);
(PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, (k!*x)^k/(1-x^k)))

Crossrefs

Cf. A036739, A062796, A217576, A346196, A348146.

Sequence in context: A235456 A159808 A159317 * A346196 A261945 A024070

Adjacent sequences: A345462 A345463 A345464 * A345466 A345467 A345468

Keyword

nonn

Author

Seiichi Manyama, Jul 10 2021

Status

approved