A165872 Totally multiplicative sequence with a(p^e) = (-2)^e.

1, -2, -2, 4, -2, 4, -2, -8, 4, 4, -2, -8, -2, 4, 4, 16, -2, -8, -2, -8, 4, 4, -2, 16, 4, 4, -8, -8, -2, -8, -2, -32, 4, 4, 4, 16, -2, 4, 4, 16, -2, -8, -2, -8, -8, 4, -2, -32, 4, -8, 4, -8, -2, 16, 4, 16, 4, 4, -2, 16, -2, 4, -8, 64, 4, -8, -2, -8, 4, -8, -2, -32, -2, 4, -8, -8, 4, -8, -2, -32, 16, 4, -2, 16, 4, 4, 4, 16

Offset: 1

Author

Jaroslav Krizek, Sep 28 2009

Keywords

• sign
• mult

Comments

The Dirichlet series is Product_{prime p} 1/(1+2/p^s), related to the Feller-Tornier constants like A065474. - R. J. Mathar, Feb 07 2011

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001222, A061142, A065474, A122803.

Programs

Mathematica

(-2)^PrimeOmega[Range[100]] (* G. C. Greubel, Apr 16 2016 *)

PARI

a(n) = (-2)^bigomega(n); \\ Altug Alkan, Apr 16 2016

Formula

a(n) = A122803(A001222(n)) = (-2)^bigomega(n) = (-2)^A001222(n).

Abs(a(n)) = A061142(n).