A154282 Dirichlet inverse of A154281.

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

Offset: 1

Author

Mats Granvik, Jan 06 2009

Keywords

• sign
• easy
• mult

Comments

Sequence is positive as often as negative.

Multiplicative because A154281 is. - Andrew Howroyd, Aug 05 2018

Links

• Mats Granvik, Table of n, a(n) for n = 1..1500

Crossrefs

Cf. A154269, A154271, A154272, A154281.

Programs

Mathematica

nn = 95; a = PadRight[{1, 0, 0, 1}, nn, 0]; Inverse[Table[Table[If[Mod[n, k] == 0, a[[n/k]], 0], {k, 1, nn}], {n, 1, nn}]][[All, 1]] (* Mats Granvik, Jul 23 2017 *)

PARI

a(n) = {my(e=valuation(n,2)); if(e%2 == 0 && n == 1<Andrew Howroyd, Aug 05 2018

Formula

Multiplicative with a(2^e) = (-1)^(e/2) if e is even and 0 is e is odd, and a(p^e) = 0 if p is an odd prime. - Amiram Eldar, Aug 27 2023