A099740 a(n) = Sum_{k|n} k!*mu(k), where mu() is the Moebius function.

1, -1, -5, -1, -119, 713, -5039, -1, -5, 3628679, -39916799, 713, -6227020799, 87178286159, 1307674367875, -1, -355687428095999, 713, -121645100408831999, 3628679, 51090942171709434955, 1124000727777567763199, -25852016738884976639999, 713, -119, 403291461126605629356979199

Offset: 1

Author

Leroy Quet, Nov 09 2004

Keywords

• sign

Comments

a(2^k)=1, a(3^k)=5, a(5^k)=119, a(6*2^i*3^j)=713, a(7^k)=5039, a(10*2^i*5^j)=3628679, etc. - Robert G. Wilson v, Nov 12 2004

Crossrefs

Cf. A000142, A008683.

Programs

Mathematica

f[n_] := Block[{k = Divisors[n]}, Plus @@ (k!MoebiusMu[k])]; Table[ f[n], {n, 25}] (* Robert G. Wilson v, Nov 12 2004 *)

PARI

a(n) = sumdiv(n, d, d!*moebius(d)); \\ Michel Marcus, Feb 19 2017

Formula

G.f.: Sum_{k>=1} mu(k)*k!*x^k/(1 - x^k). - Ilya Gutkovskiy, Feb 19 2017

Extensions

More terms from Robert G. Wilson v, Nov 12 2004