OFFSET
1,2
FORMULA
E.g.f.: Sum_{k>0} (k * x)^k/(k! - (k * x)^k).
If p is prime, a(p) = p^p + p!.
MATHEMATICA
a[n_] := n! * DivisorSum[n, #^n / #!^(n/#) &]; Array[a, 20] (* Amiram Eldar, Jul 31 2023 *)
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, (k*x)^k/(k!-(k*x)^k))))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 23 2023
STATUS
approved