OFFSET
1,2
FORMULA
a(n) = n! * Sum_{d|n} 1 / (d^(n/d-1) * d!).
If p is prime, a(p) = 1 + p! = A038507(p).
MATHEMATICA
a[n_] := n! * DivisorSum[n, 1/(#^(n/#-1) * #!) &]; 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/k)))))
(PARI) a(n) = n!*sumdiv(n, d, 1/(d^(n/d-1)*d!));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 23 2023
STATUS
approved