A355683 Multiplicative with a(p^e) = 0 if e=1 and a(p^e)= -1 if e>1.

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

Offset

1

Links

Antti Karttunen, Table of n, a(n) for n = 1..100000

Formula

a(n) = A076479(n) * A112526(n).

Mathematica

f[p_, e_] := If[e == 1, 0, -1]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Jul 14 2022 *)

Prog

(PARI) A355683(n) = factorback(apply(e -> -(e>=2), factor(n)[, 2]));

Crossrefs

Cf. A076479, A112526 (absolute values).

Sequence in context: A112526 A307423 A355684 * A120523 A269625 A359828

Adjacent sequences: A355680 A355681 A355682 * A355684 A355685 A355686

Keyword

sign,mult

Author

Antti Karttunen, Jul 14 2022, after R. J. Mathar's Apr 04 2011 comment in A112526.

Status

approved