A099740 - OEIS

%I #17 Aug 19 2022 14:20:29

%S 1,-1,-5,-1,-119,713,-5039,-1,-5,3628679,-39916799,713,-6227020799,

%T 87178286159,1307674367875,-1,-355687428095999,713,

%U -121645100408831999,3628679,51090942171709434955,1124000727777567763199,-25852016738884976639999,713,-119,403291461126605629356979199

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

%C 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

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

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

%o (PARI) a(n) = sumdiv(n, d, d!*moebius(d)); \\ _Michel Marcus_, Feb 19 2017

%Y Cf. A000142, A008683.

%K sign

%O 1,3

%A _Leroy Quet_, Nov 09 2004

%E More terms from _Robert G. Wilson v_, Nov 12 2004