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A379107 Dirichlet convolution of A033879 and A378990, where A033879 is the deficiency of n, and A378990 is the Dirichlet inverse of the binary weight of n.

%I A379107 #8 Dec 16 2024 22:19:11
%S A379107 1,0,0,0,2,-2,3,0,3,-2,7,-4,9,-2,-2,0,14,-4,15,-4,1,-2,18,-8,12,-2,4,
%T A379107 -4,24,-10,25,0,2,-2,7,-8,33,-2,0,-8,37,-12,38,-4,2,-2,41,-16,29,-8,
%U A379107 -2,-4,48,-14,13,-8,0,-2,53,-20,55,-2,-1,0,20,-20,63,-4,3,-16,66,-16,69,-2,-6,-4,24,-24,73,-16,24,-2,78
%N A379107 Dirichlet convolution of A033879 and A378990, where A033879 is the deficiency of n, and A378990 is the Dirichlet inverse of the binary weight of n.
%H A379107 Antti Karttunen, <a href="/A379107/b379107.txt">Table of n, a(n) for n = 1..20000</a>
%H A379107 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>.
%H A379107 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>.
%F A379107 a(n) = Sum_{d|n} A033879(d)*A378990(n/d).
%o A379107 (PARI)
%o A379107 A033879(n) = (n+n-sigma(n));
%o A379107 memoA378990 = Map();
%o A379107 A378990(n) = if(1==n,1,my(v); if(mapisdefined(memoA378990,n,&v), v, v = -sumdiv(n,d,if(d<n,hammingweight(n/d)*A378990(d),0)); mapput(memoA378990,n,v); (v)));
%o A379107 A379107(n) = sumdiv(n,d,A033879(d)*A378990(n/d));
%Y A379107 Cf. A000120, A033879, A378990, A379106 (Dirichlet inverse).
%Y A379107 Cf. also A294898, A378755, A378757.
%K A379107 sign
%O A379107 1,5
%A A379107 _Antti Karttunen_, Dec 16 2024