A069517 a(n) = (-1)*Sum_{d|n} (moebius(d)*(-1)^d).

1, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 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, 2, 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

Offset: 1

Author

Benoit Cloitre, Apr 16 2002

Keywords

• easy
• nonn
• mult

Comments

From Andrew Howroyd, Jul 25 2018: (Start)

Moebius transform of A037227.

Multiplicative because A037227 is. (End)

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384

Crossrefs

Cf. A037227, A209229.

Programs

Mathematica

a[n_] := If[n == 2^IntegerExponent[n, 2], 2, 0]; a[1] = 1; Array[a, 100] (* Amiram Eldar, Aug 29 2023 *)

PARI

A069517(n) = (-1)*sumdiv(n,d,moebius(d)*((-1)^d)); \\ Antti Karttunen, Nov 19 2017

PARI

a(n) = if(n == 1, 1, if(n >> valuation(n, 2) == 1, 2, 0)); \\ Amiram Eldar, Aug 29 2023

Formula

a(1) = 1 and for n>1, a(n) = 2*A209229(n). - corrected by Antti Karttunen, Nov 19 2017

Multiplicative with a(2^e) = 2 and a(p^e) = 0 for an odd prime p. - Amiram Eldar, Aug 29 2023