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

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

Offset: 1

Author

Seiichi Manyama, Jul 10 2021

Keywords

• nonn

Links

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

Crossrefs

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

Programs

Mathematica

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

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)))

Formula

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

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