A346196 a(n) = Sum_{d|n} (d!)^n.

1, 5, 217, 331793, 24883200001, 139314069504046721, 82606411253903523840000001, 6984964247141514123629140487675314433, 109110688415571316480344899355894085582848010077697, 395940866122425193243875570782668457763038823019173642240000001025

Offset: 1

Author

Seiichi Manyama, Jul 10 2021

Keywords

• nonn

Links

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

Crossrefs

Cf. A023887, A036739, A217576, A345465, A348146.

Programs

Mathematica

a[n_] := DivisorSum[n, (#!)^n &]; Array[a, 10] (* Amiram Eldar, Aug 30 2023 *)

PARI

a(n) = sumdiv(n, d, d!^n);

PARI

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

Formula

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

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