A053865 - OEIS

A053865

A third-order generalization of the Mobius function of n.

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Compares the exponents of the factors of the canonical prime factorization of n with 3 as detailed in A053864.

LINKS

R. J. Mathar, Table of n, a(n) for n = 1..1000

MATHEMATICA

a[n_] := Which[ee = FactorInteger[n][[All, 2]]; AnyTrue[ee, # > 3 &], 0, AnyTrue[ee, # < 3 &], 1, True, (-1)^Length[ee]]; Array[a, 100] (* Jean-François Alcover, Feb 09 2018 *)

PROG

(PARI) a(n) = if(n == 1, 1, my(e = factor(n)[, 2]); if(vecmax(e) > 3, 0, if(vecmin(e) < 3, 1, (-1)^#e))); \\ Amiram Eldar, Oct 01 2024

CROSSREFS

Cf. A008683, A053864, A053981.

Sequence in context: A307445 A363552 A307430 * A189022 A370598 A166234

Adjacent sequences: A053862 A053863 A053864 * A053866 A053867 A053868

KEYWORD

sign,easy

AUTHOR

N. J. A. Sloane, Apr 08 2000

STATUS

approved