A098018 a(n) = Sum_{k|n, k>=2} mu(k-1), where mu() is the Moebius function.

0, 1, -1, 0, 0, -1, 1, -1, -1, 1, 1, -3, 0, 1, 0, 0, 0, -2, 0, -1, 0, 3, 1, -5, 0, 1, 0, 0, 0, -1, -1, -1, 0, 2, 2, -3, 0, 0, 0, -1, 0, -2, -1, 1, 0, 2, 1, -5, 1, 1, -1, 1, 0, -2, 1, 0, -1, 2, 1, -5, 0, -1, 1, -1, 0, 2, -1, 0, 0, 3, -1, -6, 0, 0, 1, -1, 2, 1, -1, -1, 0, 1, 1, -5, 0, 1, 0, 1, 0, -3, 1, 2, -2, 3, 1, -5, 0, 0, 0, -1, 0, -1, -1, -1, 2

Offset: 1

Author

Leroy Quet, Oct 24 2004

Keywords

• sign

Examples

			12's divisors >=2 are 2, 3, 4, 6 and 12. So a(12) = mu(1) + mu(2) + mu(3) + mu(5) + mu(11) = 1 - 1 - 1 - 1 - 1 = -3.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A008683, A098035.

Programs

Mathematica

f[n_] := Plus @@ MoebiusMu[ Drop[ Divisors[n], 1] - 1]; Table[ f[n], {n, 105}] (* Robert G. Wilson v, Nov 01 2004 *)
Table[DivisorSum[n, MoebiusMu[# - 1] &, # > 1 &], {n, 105}] (* Michael De Vlieger, Sep 04 2017 *)

PARI

a(n)=sumdiv(n,k,if(k>1,moebius(k-1))) \\ Charles R Greathouse IV, Feb 07 2013

Extensions

More terms from Robert G. Wilson v, Nov 01 2004