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A378655 Dirichlet convolution of A153881 with the Dirichlet inverse of A103977.

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%I A378655 #7 Dec 04 2024 15:45:50
%S A378655 1,-2,-3,0,-5,6,-7,0,0,10,-11,-4,-13,14,15,0,-17,-4,-19,-2,21,22,-23,
%T A378655 0,0,26,0,0,-29,-42,-31,0,33,34,35,12,-37,38,39,-4,-41,-54,-43,0,0,46,
%U A378655 -47,0,0,0,51,0,-53,8,55,-8,57,58,-59,34,-61,62,0,0,65,-78,-67,0,69,-74,-71,-8,-73,74,0,0,77,-90,-79,0,0
%N A378655 Dirichlet convolution of A153881 with the Dirichlet inverse of A103977.
%H A378655 Antti Karttunen, <a href="/A378655/b378655.txt">Table of n, a(n) for n = 1..20000</a>
%F A378655 a(n) = Sum_{d|n} A153881(d)*A378643(n/d).
%F A378655 a(n) = A055615(n) when n is a non-abundant number (A263837), and also for some subset of the abundant numbers, A005101.
%o A378655 (PARI)
%o A378655 A153881(n) = if(n>1, -1, 1);
%o A378655 A378655(n) = sumdiv(n,d,A153881(d)*A378643(n/d));
%Y A378655 Cf. A055615, A103977, A153881, A263837, A378643, A378647 (Dirichlet inverse).
%K A378655 sign
%O A378655 1,2
%A A378655 _Antti Karttunen_, Dec 04 2024