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%I #7 Dec 03 2024 19:50:05
%S 1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,3,-1,-1,-1,-1,-1,3,-1,1,-1,-1,-1,3,
%T -1,-1,-1,-1,-1,11,-1,-1,-1,-1,-1,-1,-1,-1,-1,5,-1,11,-1,-1,-1,-1,-1,
%U 3,-1,-1,-1,-1,-1,-1,-1,7,-1,-1,-1,-3,-1,-1,-1,-1,-1,11,-1,-1,-1,3,-1,-1,-1,-1,-1,-1,-1,11,-1,5,-1,-1,-1,3
%N Dirichlet convolution of A055615 and A103977.
%H Antti Karttunen, <a href="/A378645/b378645.txt">Table of n, a(n) for n = 1..20000</a>
%F a(n) = Sum_{d|n} A055615(d)*A103977(n/d).
%F a(n) = A153881(n) always when n is a non-abundant number (A263837), and also for some of the abundant numbers, A005101.
%o (PARI)
%o A055615(n) = (n*moebius(n));
%o A378645(n) = sumdiv(n,d,A055615(d)*A103977(n/d));
%Y Cf. A055615, A263837, A103977, A153881, A378646 (Dirichlet inverse).
%K sign
%O 1,12
%A _Antti Karttunen_, Dec 03 2024