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

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 A368907

Adjacent sequences: A304650 A304651 A304652 * A304654 A304655 A304656

Keyword

sign

Author

Gus Wiseman, May 18 2018

Status

approved