A347234 - OEIS

%I #11 Sep 18 2021 22:02:27

%S 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 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 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 Dirichlet convolution of A126760 with A342001.

%H Antti Karttunen, <a href="/A347234/b347234.txt">Table of n, a(n) for n = 1..16384</a>

%H Antti Karttunen, <a href="/A347234/a347234.txt">Data supplement: n, a(n) computed for n = 1..65537</a>

%F a(n) = Sum_{d|n} A126760(d) * A342001(n/d).

%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 A003557(n) = (n/factorback(factorint(n)[, 1]));

%o A342001(n) = (A003415(n) / A003557(n));

%o A126760(n) = {n&&n\=3^valuation(n, 3)<<valuation(n, 2); n%3+n\6*2}; \\ From A126760

%o A347234(n) = sumdiv(n,d,A126760(d)*A342001(n/d));

%Y Cf. A003415, A003557, A126760, A342001.

%Y Cf. also A346485, A347233, A347235, A347395.

%K nonn

%O 1,4

%A _Antti Karttunen_, Aug 26 2021