A352058 a(n) = Sum_{p|n, p prime} n!/(p!*(n/p)!).

0, 1, 1, 6, 1, 120, 1, 840, 10080, 30240, 1, 3659040, 1, 17297280, 3632428800, 259459200, 1, 1490852563200, 1, 845092863014400, 3379030566912000, 28158588057600, 1, 2565331847811532800, 1077167364120207360000, 64764752532480000, 5001134190558105600000

Offset

1,4

Links

Table of n, a(n) for n=1..27.

Formula

E.g.f.: Sum_{p prime} (exp(x^p) - 1)/p!.

a(n) = 1 if and only if n is prime.

Mathematica

a[1] = 0; a[n_] := Plus @@ (n!/((p=FactorInteger[n][[;; , 1]])!*(n/p)!)); Array[a, 30] (* Amiram Eldar, Mar 02 2022 *)

Prog

(PARI) a(n) = my(f=factor(n)); sum(k=1, #f~, n!/(f[k, 1]!*(n/f[k, 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

Cf. A121860, A352012, A352059, A352060.

Sequence in context: A318107 A365908 A331557 * A303675 A266302 A352012

Adjacent sequences: A352055 A352056 A352057 * A352059 A352060 A352061

Keyword

nonn

Author

Seiichi Manyama, Mar 02 2022

Status

approved