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A349347 Sum of A181988 and its Dirichlet inverse, where A181988(n) = A001511(n)*A003602(n).

%I A349347 #7 Dec 09 2021 01:31:34
%S A349347 2,0,0,4,0,8,0,4,4,12,0,4,0,16,12,5,0,12,0,6,16,24,0,8,9,28,12,8,0,8,
%T A349347 0,6,24,36,24,14,0,40,28,12,0,12,0,12,26,48,0,10,16,34,36,14,0,32,36,
%U A349347 16,40,60,0,28,0,64,36,7,42,20,0,18,48,24,0,20,0,76,46,20,48,24,0,15,37,84,0,38,54,88,60,24,0,40
%N A349347 Sum of A181988 and its Dirichlet inverse, where A181988(n) = A001511(n)*A003602(n).
%H A349347 Antti Karttunen, <a href="/A349347/b349347.txt">Table of n, a(n) for n = 1..20000</a>
%F A349347 a(n) = A181988(n) + A349346(n).
%F A349347 a(1) = 2, and for n > 1, a(n) = -Sum_{d|n, 1<d<n} A181988(d) * A349346(n/d).
%o A349347 (PARI)
%o A349347 up_to = 20000;
%o A349347 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 A349347 A001511(n) = 1+valuation(n,2);
%o A349347 A003602(n) = (1+(n>>valuation(n,2)))/2;
%o A349347 A181988(n) = (A001511(n)*A003602(n));
%o A349347 v349346 = DirInverseCorrect(vector(up_to,n,A181988(n)));
%o A349347 A349346(n) = v349346[n];
%o A349347 A349347(n) = (A181988(n)+A349346(n));
%Y A349347 Cf. A001511, A003602, A181988, A349346.
%K A349347 nonn
%O A349347 1,1
%A A349347 _Antti Karttunen_, Nov 15 2021