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A347234 Dirichlet convolution of A126760 with A342001.

%I A347234 #11 Sep 18 2021 22:02:27
%S A347234 0,1,1,3,1,7,1,6,3,10,1,17,1,13,11,10,1,16,1,26,14,18,1,31,4,21,6,35,
%T A347234 1,61,1,15,19,26,17,36,1,29,22,49,1,82,1,50,28,34,1,49,5,36,27,59,1,
%U A347234 28,22,67,30,42,1,139,1,45,37,21,25,117,1,74,35,127,1,63,1,53,40,83,25,138,1,79,10,58,1,190,30,61
%N A347234 Dirichlet convolution of A126760 with A342001.
%H A347234 Antti Karttunen, <a href="/A347234/b347234.txt">Table of n, a(n) for n = 1..16384</a>
%H A347234 Antti Karttunen, <a href="/A347234/a347234.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%F A347234 a(n) = Sum_{d|n} A126760(d) * A342001(n/d).
%o A347234 (PARI)
%o A347234 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A347234 A003557(n) = (n/factorback(factorint(n)[, 1]));
%o A347234 A342001(n) = (A003415(n) / A003557(n));
%o A347234 A126760(n) = {n&&n\=3^valuation(n, 3)<<valuation(n, 2); n%3+n\6*2}; \\ From A126760
%o A347234 A347234(n) = sumdiv(n,d,A126760(d)*A342001(n/d));
%Y A347234 Cf. A003415, A003557, A126760, A342001.
%Y A347234 Cf. also A346485, A347233, A347235, A347395.
%K A347234 nonn
%O A347234 1,4
%A A347234 _Antti Karttunen_, Aug 26 2021