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A347235 Dirichlet convolution of Euler phi with A342001, where A342001(n) = A003415(n) / A003557(n).

%I A347235 #14 Sep 18 2021 22:02:39
%S A347235 0,1,1,3,1,8,1,7,4,12,1,21,1,16,14,15,1,27,1,33,18,24,1,47,6,28,13,45,
%T A347235 1,87,1,31,26,36,22,69,1,40,30,75,1,119,1,69,51,48,1,99,8,63,38,81,1,
%U A347235 84,30,103,42,60,1,219,1,64,67,63,34,183,1,105,50,183,1,153,1,76,75,117,34,215,1,159,40,84,1,303,42
%N A347235 Dirichlet convolution of Euler phi with A342001, where A342001(n) = A003415(n) / A003557(n).
%H A347235 Antti Karttunen, <a href="/A347235/b347235.txt">Table of n, a(n) for n = 1..16384</a>
%H A347235 Antti Karttunen, <a href="/A347235/a347235.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%F A347235 a(n) = Sum_{d|n} A000010(n/d) * A342001(d).
%F A347235 a(n) = Sum_{k=1..n} A342001(gcd(n,k)). - _Antti Karttunen_, Sep 02 2021
%o A347235 (PARI)
%o A347235 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A347235 A003557(n) = (n/factorback(factorint(n)[, 1]));
%o A347235 A342001(n) = (A003415(n) / A003557(n));
%o A347235 A347235(n) = sumdiv(n,d,eulerphi(d)*A342001(n/d));
%o A347235 (PARI) A347235(n) = sum(k=1,n,A342001(gcd(n,k))); \\ (Slow) - _Antti Karttunen_, Sep 02 2021
%Y A347235 Cf. A000010, A003415, A003557, A342001.
%Y A347235 Cf. also A346485, A347131, A347233, A347234, A347395.
%K A347235 nonn
%O A347235 1,4
%A A347235 _Antti Karttunen_, Aug 26 2021