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%I #26 Dec 11 2020 03:58:59
%S 1,2,8,24,80,232,728,2160,6552,19600,59048,176880,531440,1593592,
%T 4782880,14346720,43046720,129133368,387420488,1162241760,3486783664,
%U 10460294152,31381059608,94142999520,282429536400,847288078000,2541865821768,7625595890640,22876792454960
%N Dirichlet convolution of mu(n) with 3^(n-1).
%H Seiichi Manyama, <a href="/A034741/b034741.txt">Table of n, a(n) for n = 1..2096</a>
%F G.f.: Sum_{k>=1} mu(k)*x^k/(1 - 3*x^k). - _Ilya Gutkovskiy_, Oct 25 2018
%F a(n) ~ 3^(n-1). - _Vaclav Kotesovec_, Sep 11 2019
%t 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 *)
%o (PARI) a(n) = sumdiv(n,d, moebius(d) * 3^(n/d-1) ); \\ _Joerg Arndt_, Apr 14 2013
%Y Column k=3 of A143325.
%Y First differences of A320087.
%Y Cf. A054718.
%K nonn
%O 1,2
%A _Erich Friedman_
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