A347389 Dirichlet convolution of A003415(n) and A003415(A276086(n)), where A003415(n) is the arithmetic derivative of n, and A276086(n) gives the prime product form of primorial base expansion of n.

0, 1, 1, 5, 1, 11, 1, 22, 11, 29, 1, 48, 1, 17, 34, 76, 1, 84, 1, 160, 22, 137, 1, 172, 31, 61, 88, 130, 1, 404, 1, 456, 142, 725, 40, 411, 1, 297, 66, 900, 1, 1262, 1, 1984, 421, 4001, 1, 1244, 21, 1866, 730, 2382, 1, 6574, 160, 8740, 302, 22157, 1, 1930, 1, 43, 1249, 1530, 84, 2222, 1, 2968, 4006, 568, 1, 1860

Offset: 1

Author

Antti Karttunen, Sep 02 2021

Keywords

• nonn
• base
• look

Links

• Antti Karttunen, Table of n, a(n) for n = 1..2309
• Index entries for sequences related to primorial base

Crossrefs

Cf. A003415, A276086, A327860.

Cf. also A345000.

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); };
A347389(n) = sumdiv(n,d,A003415(n/d) * A003415(A276086(d)));

Formula

a(n) = Sum_{d|n} A003415(n/d) * A327860(d).