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A347958 Inverse Möbius transform of A345000.

%I A347958 #10 Oct 15 2021 21:34:34
%S A347958 1,2,2,4,2,4,2,8,3,4,2,8,2,4,4,24,2,8,2,8,8,4,2,16,7,8,4,8,2,8,2,34,4,
%T A347958 4,6,24,2,4,4,14,2,12,2,10,6,8,2,34,3,14,8,14,2,12,4,14,4,4,2,16,2,4,
%U A347958 10,46,6,8,2,8,4,10,2,44,2,4,64,16,6,12,2,46,5,4,2,20,4,8,4,154,2,16,4,26,4,52,6,46
%N A347958 Inverse Möbius transform of A345000.
%H A347958 Antti Karttunen, <a href="/A347958/b347958.txt">Table of n, a(n) for n = 1..10000</a>
%H A347958 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%F A347958 a(n) = Sum_{d|n} A345000(d).
%o A347958 (PARI)
%o A347958 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A347958 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A347958 A345000(n) = gcd(A003415(n), A003415(A276086(n)));
%o A347958 A347958(n) = sumdiv(n,d,A345000(d));
%Y A347958 Cf. A003415, A276086, A327860, A345000, A347959.
%K A347958 nonn,base
%O A347958 1,2
%A A347958 _Antti Karttunen_, Sep 21 2021