A354892 a(n) = n! * Sum_{d|n} d^n / (n/d)!.

1, 9, 163, 6337, 375001, 33862441, 4150656721, 677778984961, 140588337476161, 36305718780965761, 11388728893445164801, 4271349071581227377281, 1886009588552176549862401, 968755330019156299208709121, 572622623006183707899105964801

Offset: 1

Author

Seiichi Manyama, Jun 10 2022

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..232

Crossrefs

Cf. A354843, A354890.

Programs

Mathematica

a[n_] := n! * DivisorSum[n, #^n/(n/#)! &]; Array[a, 15] (* Amiram Eldar, Jun 10 2022 *)

PARI

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

PARI

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

Formula

E.g.f.: Sum_{k>0} (exp((k * x)^k) - 1).

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