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A378756 Dirichlet convolution of A046692 and A005187, where A046692 is the Dirichlet inverse of sigma.

%I A378756 #7 Dec 15 2024 21:09:28
%S A378756 1,0,0,0,2,-2,3,0,3,-6,7,0,9,-8,-6,0,14,-6,15,0,-5,-16,18,0,4,-20,-2,
%T A378756 0,24,14,25,0,-12,-30,-15,0,33,-32,-18,0,37,12,38,0,-12,-38,41,0,14,
%U A378756 -8,-30,0,48,4,-33,0,-30,-50,53,0,55,-52,-27,0,-38,26,63,0,-33,32,66,0,69,-68,-6,0,-38,38,73,0,7,-76,78
%N A378756 Dirichlet convolution of A046692 and A005187, where A046692 is the Dirichlet inverse of sigma.
%H A378756 Antti Karttunen, <a href="/A378756/b378756.txt">Table of n, a(n) for n = 1..20000</a>
%H A378756 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A378756 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A378756 a(n) = Sum_{d|n} A046692(d)*A005187(n/d).
%o A378756 (PARI)
%o A378756 A005187(n) = { my(s=n); while(n>>=1, s+=n); s; };
%o A378756 A046692(n) = { my(f=factor(n)~); prod(i=1, #f, if(1==f[2,i], -(f[1,i]+1), if(2==f[2,i], f[1,i], 0))); };
%o A378756 A378756(n) = sumdiv(n,d,A046692(d)*A005187(n/d));
%Y A378756 Cf. A005187, A046692, A378757 (Dirichlet inverse).
%Y A378756 Cf. also A294898.
%K A378756 sign
%O A378756 1,5
%A A378756 _Antti Karttunen_, Dec 15 2024