A062794 Moebius transform of n!.

1, 1, 5, 22, 119, 713, 5039, 40296, 362874, 3628679, 39916799, 479000858, 6227020799, 87178286159, 1307674367875, 20922789847680, 355687428095999, 6402373705364406, 121645100408831999, 2432902008173011178

Offset: 1

Author

Labos Elemer, Jul 19 2001

Keywords

• nonn

Comments

n=5, f[5]=120, divisors={1,5} f[5/d]={120,1}, mu[d]={1,-1}, the sum is 120-1=119=a(5)

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..449

Crossrefs

Cf. A000142, A008683.

Programs

PARI

a(n) = sumdiv(n, d, d!*moebius(n/d)); \\ Michel Marcus, Nov 04 2018

Formula

a(n) = Sum{f[n/d]*mu[d]}, where d|n and f[x]=A000142(x).

a(n) ~ n!. - Vaclav Kotesovec, Sep 16 2021