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Dirichlet convolution of A055615 and A103977.
4

%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