A347958 Inverse Möbius transform of A345000.

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, 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, 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

Offset: 1

Author

Antti Karttunen, Sep 21 2021

Keywords

• nonn
• base

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to primorial base

Crossrefs

Cf. A003415, A276086, A327860, A345000, A347959.

Programs

PARI

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A345000(n) = gcd(A003415(n), A003415(A276086(n)));
A347958(n) = sumdiv(n,d,A345000(d));

Formula

a(n) = Sum_{d|n} A345000(d).