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A378757 Dirichlet convolution of sigma and the Dirichlet inverse of A005187 (A346237).

%I A378757 #7 Dec 15 2024 21:09:34
%S A378757 1,0,0,0,-2,2,-3,0,-3,6,-7,0,-9,8,6,0,-14,6,-15,0,5,16,-18,0,0,20,2,0,
%T A378757 -24,-22,-25,0,12,30,27,4,-33,32,18,0,-37,-24,-38,0,24,38,-41,0,-5,
%U A378757 -16,30,0,-48,-16,61,0,30,50,-53,24,-55,52,45,0,74,-54,-63,0,33,-100,-66,0,-69,68,-18,0,80,-74,-73,0,2,76,-78
%N A378757 Dirichlet convolution of sigma and the Dirichlet inverse of A005187 (A346237).
%H A378757 Antti Karttunen, <a href="/A378757/b378757.txt">Table of n, a(n) for n = 1..20000</a>
%H A378757 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A378757 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A378757 a(n) = Sum_{d|n} A000203(d)*A346237(n/d).
%o A378757 (PARI)
%o A378757 A005187(n) = { my(s=n); while(n>>=1, s+=n); s; };
%o A378757 memoA346237 = Map();
%o A378757 A346237(n) = if(1==n,1,my(v); if(mapisdefined(memoA346237,n,&v), v, v = -sumdiv(n,d,if(d<n,A005187(n/d)*A346237(d),0)); mapput(memoA346237,n,v); (v)));
%o A378757 A378757(n) = sumdiv(n,d,sigma(d)*A346237(n/d));
%Y A378757 Cf. A000203, A005187, A346237, A378756 (Dirichlet inverse).
%Y A378757 Cf. also A294898.
%K A378757 sign
%O A378757 1,5
%A A378757 _Antti Karttunen_, Dec 15 2024