A352060 a(n) = (n - 1)! * omega(n), where omega(n) = number of distinct primes dividing n (A001221).

0, 1, 2, 6, 24, 240, 720, 5040, 40320, 725760, 3628800, 79833600, 479001600, 12454041600, 174356582400, 1307674368000, 20922789888000, 711374856192000, 6402373705728000, 243290200817664000, 4865804016353280000, 102181884343418880000, 1124000727777607680000

Offset

1,3

Links

Table of n, a(n) for n=1..23.

Formula

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

Mathematica

a[n_] := (n-1)! * PrimeNu[n]; Array[a, 25] (* Amiram Eldar, Mar 02 2022 *)

Prog

(PARI) a(n) = (n-1)!*omega(n);
(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

Cf. A001221, A318249, A352012, A352058, A352059.

Sequence in context: A034874 A052699 A074351 * A346121 A052597 A052632

Adjacent sequences: A352057 A352058 A352059 * A352061 A352062 A352063

Keyword

nonn

Author

Seiichi Manyama, Mar 02 2022

Status

approved