OFFSET
1,3
FORMULA
E.g.f.: Sum_{p prime} (exp(x^p) - 1)/p.
MATHEMATICA
a[1] = 0; a[n_] := Plus @@ ((n-1)!/(n/FactorInteger[n][[;; , 1]] - 1)!); Array[a, 25] (* Amiram Eldar, Mar 02 2022 *)
PROG
(PARI) a(n) = my(f=factor(n)); sum(k=1, #f~, (n-1)!/(n/f[k, 1]-1)!);
(PARI) my(N=40, x='x+O('x^N)); concat(0, Vec(serlaplace(sum(k=1, N, isprime(k)*(exp(x^k)-1)/k))))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 02 2022
STATUS
approved