A304653 - OEIS

A304653

a(n) = (-1)^Omega(n) if n is not a perfect power > 1, and 0 otherwise.

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

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OFFSET

COMMENTS

Omega(n) = A001222(n) is the number of prime factors of n counted with multiplicity.

LINKS

Table of n, a(n) for n=1..74.

EXAMPLE

Agrees with Moebius function A008683 except for numbers like 12, 18, .... Moebius(12) = 0, a(12) = (-1)^3 = -1. - N. J. A. Sloane, May 26 2018

MATHEMATICA

Table[If[GCD @@ FactorInteger[n][[All, 2]] == 1, (-1)^PrimeOmega[n], 0], {n, 100}]

CROSSREFS

An unsigned version is A132350.