A354893 a(n) = n! * Sum_{d|n} d^(n - d) / (n/d)!.

1, 3, 7, 73, 121, 12361, 5041, 5308801, 44452801, 5681370241, 39916801, 16800125569921, 6227020801, 35897693762810881, 2134168822456070401, 190139202281277849601, 355687428096001, 3563095308471181273190401, 121645100408832001

Offset: 1

Author

Seiichi Manyama, Jun 10 2022

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..291

Crossrefs

Cf. A038507, A342628, A354845, A354891, A354892.

Programs

Mathematica

a[n_] := n! * DivisorSum[n, #^(n - #)/(n/#)! &]; Array[a, 19] (* Amiram Eldar, Jun 10 2022 *)

PARI

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

PARI

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

Formula

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

If p is prime, a(p) = 1 + p! = A038507(p).