A084846 mu(n!+1), where mu is the Moebius function (A008683).

-1, -1, -1, -1, 0, 0, 1, 0, 1, -1, 1, -1, 0, 1, 1, -1, -1, -1, 1, 1, 1, -1, -1, 0, 1, 1, 1, -1, 1, -1, -1, 1, 1, -1, 1, -1, 1, -1, 1, 1, -1, -1, -1, 1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, -1, 1, -1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, 1, -1, 1, -1, 1, 1, 1, -1, 1, -1, 1, 1, -1, -1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, 1

Offset: 0

Author

Rick L. Shepherd, Jun 10 2003

Keywords

• hard
• sign

Examples

			a(6)=1 because 6!+1 = 721 = 7 * 103, the product of two different primes and thus mu(6!+1) = (-1)^2 = 1.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 0..139
• Paul Leyland, Factors of n!+1.
• Markus Tervooren et al., Factorization of n!+1, FactorDB.

Crossrefs

Cf. A008683 (mu(n)), A054990 (bigomega(n!+1)), A066856 (omega(n!+1)), A064237 (n!+1 divisible by a square), A002981 (n!+1 is prime).

Programs

Magma

[MoebiusMu(Factorial(n)+1) : n in [1..45]];

Mathematica

MoebiusMu[Range[0, 50]! + 1] (* Paolo Xausa, Feb 07 2025 *)

PARI

for(n=0,45,print1(moebius(n!+1),","))

Formula

If n is in A064237, then a(n) = 0. Otherwise a(n) = (-1)^A054990(n) = (-1)^A066856(n). - Max Alekseyev, Oct 08 2019

Extensions

a(112) corrected, a(113)-a(114) added by Max Alekseyev, May 28 2015

a(106)-a(107) corrected by Amiram Eldar, Oct 03 2019