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%I #13 Nov 26 2021 11:13:41
%S 0,1,1,1,1,-2,1,0,2,-2,1,-3,1,-2,-2,-4,1,-5,1,-3,-2,-2,1,-4,4,-2,3,-3,
%T 1,3,1,-16,-2,-2,-2,-7,1,-2,-2,-4,1,3,1,-3,-5,-2,1,-4,6,-9,-2,-3,1,
%U -12,-2,-4,-2,-2,1,5,1,-2,-5,-48,-2,3,1,-3,-2,3,1,-8,1,-2,-9,-3,-2,3,1,-4,0,-2,1,5,-2,-2,-2,-4
%N Dirichlet convolution of A003415 with the Dirichlet inverse of A003959.
%H Antti Karttunen, <a href="/A349621/b349621.txt">Table of n, a(n) for n = 1..20000</a>
%F a(n) = Sum_{d|n} A003415(n/d) * A063441(d).
%t f[p_, e_] := e/p; d[1] = 0; d[n_] := n*Plus @@ f @@@ FactorInteger[n]; a[n_] := DivisorSum[n, MoebiusMu[#] * DivisorSigma[1, #] * d[n/#] &]; Array[a, 100] (* _Amiram Eldar_, Nov 25 2021 *)
%o (PARI)
%o A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A063441(n) = (moebius(n)*sigma(n)); \\ Also Dirichlet inverse of A003959.
%o A349621(n) = sumdiv(n,d,A003415(n/d)*A063441(d));
%Y Cf. A003415, A003959, A063441.
%Y Cf. also A349173, A349394, A349618, A349619, A349620.
%K sign
%O 1,6
%A _Antti Karttunen_, Nov 25 2021
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