OFFSET
1,2
FORMULA
E.g.f.: Sum_{k>0} (exp(k * x^k) - 1)/k!.
If p is prime, a(p) = 1 + p.
MATHEMATICA
a[n_] := n! * DivisorSum[n, (n/#)^#/(#! * (n/#)!) &]; Array[a, 25] (* Amiram Eldar, Jun 08 2022 *)
PROG
(PARI) a(n) = n!*sumdiv(n, d, (n/d)^d/(d!*(n/d)!));
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, (exp(k*x^k)-1)/k!)))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jun 08 2022
STATUS
approved