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A347963 Dirichlet convolution of A342001 with A003557.

%I A347963 #7 Oct 15 2021 21:33:37
%S A347963 0,1,1,3,1,7,1,7,3,9,1,18,1,11,10,15,1,18,1,24,12,15,1,40,3,17,8,30,1,
%T A347963 54,1,31,16,21,14,45,1,23,18,54,1,68,1,42,27,27,1,84,3,24,22,48,1,48,
%U A347963 18,68,24,33,1,132,1,35,33,63,20,96,1,60,28,90,1,99,1,41,27,66,20,110,1,114,22,45,1,168,24,47
%N A347963 Dirichlet convolution of A342001 with A003557.
%H A347963 Antti Karttunen, <a href="/A347963/b347963.txt">Table of n, a(n) for n = 1..16384</a>
%F A347963 a(n) = Sum_{d|n} A003557(d) * A342001(n/d).
%o A347963 (PARI)
%o A347963 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A347963 A003557(n) = (n/factorback(factorint(n)[, 1]));
%o A347963 A342001(n) = (A003415(n) / A003557(n));
%o A347963 A347963(n) = sumdiv(n,d,A003557(n/d)*A342001(d));
%Y A347963 Cf. A003415, A003557, A342001.
%Y A347963 Cf. also A347961.
%K A347963 nonn
%O A347963 1,4
%A A347963 _Antti Karttunen_, Sep 24 2021