A354843 a(n) = n! * Sum_{d|n} (n/d)^d / d!.

1, 5, 19, 145, 601, 8521, 35281, 672001, 4898881, 82615681, 439084801, 21138606721, 80951270401, 3358578263041, 49506372115201, 1227603183206401, 6046686277632001, 611515751899852801, 2311256907767808001, 254421414038266675201, 4015778465971464192001

Offset: 1

Author

Seiichi Manyama, Jun 08 2022

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..447

Crossrefs

Cf. A057625, A327579, A354845.

Programs

Mathematica

a[n_] := n! * DivisorSum[n, (n/#)^#/#! &]; Array[a, 20] (* Amiram Eldar, Jun 08 2022 *)

PARI

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

PARI

my(N=30, 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!.