A359425 Dirichlet convolution of the arithmetic derivative with the primorial base exp-function.

0, 2, 2, 11, 2, 19, 2, 45, 18, 35, 2, 85, 2, 31, 40, 151, 2, 125, 2, 195, 36, 119, 2, 313, 38, 83, 120, 215, 2, 418, 2, 649, 124, 491, 52, 628, 2, 295, 88, 1057, 2, 1046, 2, 1629, 414, 2303, 2, 1777, 38, 1541, 496, 2241, 2, 4424, 140, 6421, 300, 11315, 2, 2048, 2, 83, 1002, 2013, 104, 1864, 2, 2073

Offset: 1

Author

Antti Karttunen, Jan 02 2023

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, A359425, A347130, A383286.

Cf. also A347389, 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); };
A359425(n) = sumdiv(n,d,A003415(n/d)*A276086(d));

Formula

a(n) = Sum_{d|n} A003415(n/d) * A276086(d).

a(n) = Sum_{d|n} A347130(n/d) * A383286(d). - Antti Karttunen, May 14 2025