A098035 a(n) = Sum_{d|n} mu(d+1), where mu() is the Moebius function.

-1, -2, -1, -3, 0, -3, -1, -3, 0, -2, -1, -5, 0, -1, 0, -4, -1, -3, -1, -2, 0, -3, -1, -5, 1, -1, 0, -3, -2, -4, -1, -3, 0, -1, 0, -6, 0, -1, 0, -3, -2, -2, -1, -4, 2, -3, -1, -6, -1, 0, -1, -3, -1, -2, 0, -2, 0, -4, -1, -6, 0, -2, 1, -2, 0, -4, -1, -1, -2, -2, -1, -7, 0, -1, 1, -1, -2, -3, -1, -4, 1, -4, -1, -4, 1, -1, -2, -5, -1, -2, 0, -3, 0, -1

Offset

1,2

Links

R. J. Mathar, Table of n, a(n) for n = 1..10000

Example

The divisors of 12 are 1, 2, 3, 4, 6 and 12. So a(12) = mu(2) + mu(3) + mu(4) + mu(5) + mu(7) + mu(13) = -1 - 1 + 0 - 1 - 1 - 1 = -5.

Mathematica

a[n_] := Plus @@ MoebiusMu[Divisors[n] + 1]; Table[ a[n], {n, 105}] (* Robert G. Wilson v, Nov 01 2004 *)

Prog

(PARI) a(n) = sumdiv(n, d, moebius(d+1)); \\ Amiram Eldar, Jun 06 2025

Crossrefs

Cf. A008683, A098018.

Sequence in context: A329647 A364235 A146094 * A079055 A122170 A066029

Adjacent sequences: A098032 A098033 A098034 * A098036 A098037 A098038

Keyword

sign

Author

Leroy Quet, Oct 24 2004

Extensions

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

Status

approved