A034741 - OEIS

A034741

Dirichlet convolution of mu(n) with 3^(n-1).

1, 2, 8, 24, 80, 232, 728, 2160, 6552, 19600, 59048, 176880, 531440, 1593592, 4782880, 14346720, 43046720, 129133368, 387420488, 1162241760, 3486783664, 10460294152, 31381059608, 94142999520, 282429536400, 847288078000, 2541865821768, 7625595890640, 22876792454960

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OFFSET

1,2

LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..2096

FORMULA

G.f.: Sum_{k>=1} mu(k)*x^k/(1 - 3*x^k). - Ilya Gutkovskiy, Oct 25 2018

a(n) ~ 3^(n-1). - Vaclav Kotesovec, Sep 11 2019

MATHEMATICA

nmax = 20; Rest[CoefficientList[Series[Sum[MoebiusMu[k] * x^k / (1 - 3*x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Dec 11 2020 *)

PROG

(PARI) a(n) = sumdiv(n, d, moebius(d) * 3^(n/d-1) ); \\ Joerg Arndt, Apr 14 2013