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A304653 a(n) = (-1)^Omega(n) if n is not a perfect power > 1, and 0 otherwise. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1

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.

Cf. A000005, A000961, A001221, A001222, A001597, A005117, A007916, A008683, A091050, A126706, A303554, A304326, A304362, A304779, A304817, A304819.

Sequence in context: A267708 A167021 A267687 * A132350 A076213 A120525

Adjacent sequences:  A304650 A304651 A304652 * A304654 A304655 A304656

KEYWORD

sign

AUTHOR

Gus Wiseman, May 18 2018

STATUS

approved

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Last modified October 18 02:23 EDT 2019. Contains 328135 sequences. (Running on oeis4.)