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A347396 a(n) = A347395(A276086(n)), where A347395 is Dirichlet convolution of Liouville's lambda with A342001.

%I A347396 #12 Oct 15 2021 21:38:26
%S A347396 0,1,1,3,1,2,1,5,6,14,5,9,1,2,3,5,2,3,2,6,8,16,6,10,2,3,5,7,3,4,1,7,8,
%T A347396 20,7,13,10,34,44,92,34,58,7,13,20,32,13,19,16,40,56,104,40,64,13,19,
%U A347396 32,44,19,25,1,2,3,5,2,3,5,9,14,22,9,13,2,3,5,7,3,4,6,10,16,24,10,14,3,4,7,9,4,5,2,8,10,22
%N A347396 a(n) = A347395(A276086(n)), where A347395 is Dirichlet convolution of Liouville's lambda with A342001.
%C A347396 The scatter plot looks quite peculiar. - _Antti Karttunen_, Sep 20 2021
%H A347396 Antti Karttunen, <a href="/A347396/b347396.txt">Table of n, a(n) for n = 0..11550</a>
%H A347396 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%o A347396 (PARI)
%o A347396 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A347396 A003557(n) = (n/factorback(factorint(n)[, 1]));
%o A347396 A342001(n) = (A003415(n) / A003557(n));
%o A347396 A008836(n) = ((-1)^bigomega(n));
%o A347396 A347395(n) = sumdiv(n,d,A008836(n/d)*A342001(d));
%o A347396 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A347396 A347396(n) = A347395(A276086(n));
%Y A347396 Cf. A003415, A003557, A008836, A276086, A342001, A347395.
%Y A347396 Cf. also A342002, A346471, A347126, A347232, A347962.
%K A347396 nonn,base,look
%O A347396 0,4
%A A347396 _Antti Karttunen_, Sep 02 2021