A080323 a(n) = mu(n)^n, where mu is the Moebius function (A008683).

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

Offset: 1

Author

Reinhard Zumkeller, Feb 14 2003

Keywords

• sign
• easy

Comments

Not multiplicative: a(2)*a(3) <> a(6), for example. - R. J. Mathar, Mar 31 2012

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16385

Crossrefs

Cf. A008683, A008966 (gives the absolute values), A056912, A080324, A099991, A379966.

Programs

Magma

[ MoebiusMu(n)^n : n in [1..100]];

Mathematica

Table[MoebiusMu[n]^n,{n,100}] (* Harvey P. Dale, Sep 09 2019 *)

PARI

a(n) = moebius(n)^n; \\ Michel Marcus, Sep 14 2017

Formula

a(A056912(n)) < 0; a(A080324(n)) > 0.

a(n) = A379966(n) - A099991(n). - Amiram Eldar, May 17 2025