A378655 - OEIS

%I #7 Dec 04 2024 15:45:50

%S 1,-2,-3,0,-5,6,-7,0,0,10,-11,-4,-13,14,15,0,-17,-4,-19,-2,21,22,-23,

%T 0,0,26,0,0,-29,-42,-31,0,33,34,35,12,-37,38,39,-4,-41,-54,-43,0,0,46,

%U -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 Dirichlet convolution of A153881 with the Dirichlet inverse of A103977.

%H Antti Karttunen, <a href="/A378655/b378655.txt">Table of n, a(n) for n = 1..20000</a>

%F a(n) = Sum_{d|n} A153881(d)*A378643(n/d).

%F a(n) = A055615(n) when n is a non-abundant number (A263837), and also for some subset of the abundant numbers, A005101.

%o (PARI)

%o A153881(n) = if(n>1, -1, 1);

%o A378655(n) = sumdiv(n,d,A153881(d)*A378643(n/d));

%Y Cf. A055615, A103977, A153881, A263837, A378643, A378647 (Dirichlet inverse).

%K sign

%O 1,2

%A _Antti Karttunen_, Dec 04 2024