OFFSET
1,2
FORMULA
a(n) = n! * Sum_{d|n} 1/(d-1)!^(n/d).
If p is prime, a(p) = p + p!.
MATHEMATICA
a[n_] := n! * DivisorSum[n, 1/(#-1)!^(n/#) &]; Array[a, 20] (* Amiram Eldar, Jul 31 2023 *)
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, x^k/((k-1)!-x^k))))
(PARI) a(n) = n!*sumdiv(n, d, 1/(d-1)!^(n/d));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 23 2023
STATUS
approved