OFFSET
1,4
FORMULA
E.g.f.: Sum_{p prime} log(1+x^p)/p!.
MATHEMATICA
a[n_] := Sum[(-1)^(n/p + 1)*(n - 1)!/(p - 1)!, {p, FactorInteger[n][[;; , 1]]}]; a[1] = 0; Array[a, 25] (* Amiram Eldar, Oct 04 2023 *)
PROG
(PARI) a(n) = sumdiv(n, d, isprime(d)*(-1)^(n/d+1)*(n-1)!/(d-1)!);
(PARI) my(N=40, x='x+O('x^N)); concat(0, Vec(serlaplace(sum(k=1, N, isprime(k)*log(1+x^k)/k!))))
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Feb 28 2022
STATUS
approved