OFFSET
1,2
FORMULA
E.g.f.: Sum_{k>0} (exp((k * x)^k) - 1)/k!.
If p is prime, a(p) = 1 + p^p.
MATHEMATICA
a[n_] := n! * DivisorSum[n, #^n/(#! * (n/#)!) &]; Array[a, 18] (* Amiram Eldar, Jun 11 2022 *)
PROG
(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!)))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jun 11 2022
STATUS
approved