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A349354 Sum of A328203 and its Dirichlet inverse.

%I A349354 #8 Nov 21 2021 10:16:51
%S A349354 2,0,0,4,0,20,0,8,25,32,0,20,0,44,80,16,0,30,0,32,110,68,0,40,64,80,
%T A349354 75,44,0,8,0,32,170,104,176,80,0,116,200,64,0,12,0,68,140,140,0,80,
%U A349354 121,84,260,80,0,146,272,88,290,176,0,168,0,188,195,64,320,20,0,104,350,24,0,160,0,224,242,116,374,24,0
%N A349354 Sum of A328203 and its Dirichlet inverse.
%H A349354 Antti Karttunen, <a href="/A349354/b349354.txt">Table of n, a(n) for n = 1..20000</a>
%F A349354 a(n) = A328203(n) + A349353(n).
%F A349354 a(1) = 2, and for n > 1, a(n) = -Sum_{d|n, 1<d<n} A328203(d) * A349353(n/d).
%o A349354 (PARI)
%o A349354 up_to = 20000;
%o A349354 DirInverseCorrect(v) = { my(u=vector(#v)); u[1] = (1/v[1]); for(n=2, #v, u[n] = (-u[1]*sumdiv(n, d, if(d<n, v[n/d]*u[d], 0)))); (u) }; \\ Compute the Dirichlet inverse of the sequence given in input vector v.
%o A349354 A328203(n) = if(n%2,(1/2)*(sigma(n)+(n*numdiv(n))),2*A328203(n/2));
%o A349354 v349353 = DirInverseCorrect(vector(up_to,n,A328203(n)));
%o A349354 A349353(n) = v349353[n];
%o A349354 A349354(n) = (A328203(n)+A349353(n));
%Y A349354 Cf. A328203, A349353.
%K A349354 nonn
%O A349354 1,1
%A A349354 _Antti Karttunen_, Nov 15 2021