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A347959 Dirichlet convolution of A342001 with A345000.

%I A347959 #9 Oct 15 2021 21:35:01
%S A347959 0,1,1,3,1,7,1,7,3,9,1,18,1,11,10,15,1,16,1,24,12,15,1,40,3,17,6,30,1,
%T A347959 54,1,39,16,21,14,41,1,23,18,54,1,72,1,42,25,27,1,92,3,24,22,52,1,30,
%U A347959 18,68,24,33,1,132,1,35,35,73,20,96,1,60,28,92,1,99,1,41,27,66,20,114,1,120,10,45,1,176,24,47
%N A347959 Dirichlet convolution of A342001 with A345000.
%H A347959 Antti Karttunen, <a href="/A347959/b347959.txt">Table of n, a(n) for n = 1..11550</a>
%H A347959 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%F A347959 a(n) = Sum_{d|n} A342001(n/d) * A345000(d).
%o A347959 (PARI)
%o A347959 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A347959 A003557(n) = (n/factorback(factorint(n)[, 1]));
%o A347959 A342001(n) = (A003415(n) / A003557(n));
%o A347959 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A347959 A345000(n) = gcd(A003415(n), A003415(A276086(n)));
%o A347959 A347959(n) = sumdiv(n,d,A342001(n/d)*A345000(d));
%Y A347959 Cf. A003415, A327860, A342001, A345000.
%Y A347959 Cf. also A347234, A347954, A347958.
%K A347959 nonn,base
%O A347959 1,4
%A A347959 _Antti Karttunen_, Sep 21 2021