A087989 a(n) = M(n!), the value of Mertens's function at the n-th factorial.

1, 1, 0, -1, -2, -3, -3, -6, -15, -138, -26, -527, -3474, -19550, -20014, 3084, -1253696, 7121000, -18636176, -44667415, 94933922, -848322099

Offset: 0

Author

Labos Elemer, Oct 02 2003

Keywords

• more
• sign

Examples

			a(4) = A002321(4!) = A002321(24) = -2.
		

Links

• Marc Deléglise and Joël Rivat, Computing the summation of the Mobius function, Experiment. Math. 5:4 (1996), pp. 291-295.

Crossrefs

Cf. A000142, A002321, A084237, A087987.

Programs

Mathematica

s=0; i=1; Do[While[i<= n!, s=s+MoebiusMu[i]; i++ ]; Print[s], {n, 0, 10}]

PARI

a(n)=sum(k=1,n!,moebius(k)) \\ Charles R Greathouse IV, Apr 02 2014

Formula

a(n) = A002321(A000142(n)).

Extensions

More terms from Sean A. Irvine, Dec 06 2009

a(14) from Donovan Johnson, Jun 21 2012

a(15)-a(17) from Rikard Nordgren, Nov 10 2012

a(18)-a(21) from Henri Lifchitz, Nov 10 2024