A347959 Dirichlet convolution of A342001 with A345000.

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, 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, 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

Offset: 1

Author

Antti Karttunen, Sep 21 2021

Keywords

• nonn
• base

Links

• Antti Karttunen, Table of n, a(n) for n = 1..11550
• Index entries for sequences related to primorial base

Crossrefs

Cf. A003415, A327860, A342001, A345000.

Cf. also A347234, A347954, A347958.

Programs

PARI

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A003557(n) = (n/factorback(factorint(n)[, 1]));
A342001(n) = (A003415(n) / A003557(n));
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)));
A347959(n) = sumdiv(n,d,A342001(n/d)*A345000(d));

Formula

a(n) = Sum_{d|n} A342001(n/d) * A345000(d).