OFFSET
1,2
FORMULA
E.g.f.: Sum_{k>0} k^k * (exp(x^k) - 1).
If p is prime, a(p) = 1 + p^p * p!.
MATHEMATICA
a[n_] := n! * DivisorSum[n, #^#/(n/#)! &]; Array[a, 15] (* Amiram Eldar, Jun 11 2022 *)
PROG
(PARI) a(n) = n!*sumdiv(n, d, d^d/(n/d)!);
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, k^k*(exp(x^k)-1))))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jun 11 2022
STATUS
approved