A076544 - OEIS

A076544

a(n) = mu(n) + sqf(n) where mu(n) is Moebius function, sqf(n) = 1 if n is squarefree and sqf(n) = -1 otherwise.

2, 0, 0, -1, 0, 2, 0, -1, -1, 2, 0, -1, 0, 2, 2, -1, 0, -1, 0, -1, 2, 2, 0, -1, -1, 2, -1, -1, 0, 0, 0, -1, 2, 2, 2, -1, 0, 2, 2, -1, 0, 0, 0, -1, -1, 2, 0, -1, -1, -1, 2, -1, 0, -1, 2, -1, 2, 2, 0, -1, 0, 2, -1, -1, 2, 0, 0, -1, 2, 0, 0, -1, 0, 2, -1, -1, 2, 0, 0, -1, -1, 2, 0, -1, 2, 2, 2, -1, 0, -1, 2, -1, 2, 2, 2, -1, 0, -1, -1, -1

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OFFSET

1,1

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000

Index entries for sequences computed from exponents in factorization of n.

FORMULA

a(n) = mu(n) + -1^(1+abs(mu(n))), where mu(n) = A008683(n). - Antti Karttunen, Jul 26 2017

From Amiram Eldar, May 28 2025: (Start)

a(n) = 2*mu(n)^2 + mu(n) - 1, where mu(n) = A008683(n).

Asymptotic mean: lim_{m->oo} (1/m) * Sum_{k=1..m} = 12/Pi^2 - 1. (End)

MATHEMATICA