A351230 Numerator of A003415(n) / A276086(n), where A003415 is the arithmetic derivative and A276086 is the primorial base exp-function.

0, 0, 1, 1, 4, 1, 1, 1, 4, 1, 7, 1, 16, 1, 3, 4, 32, 1, 21, 1, 8, 1, 13, 1, 44, 1, 1, 9, 32, 1, 31, 1, 80, 1, 19, 2, 12, 1, 1, 8, 68, 1, 41, 1, 16, 13, 1, 1, 16, 1, 3, 2, 8, 1, 81, 8, 92, 11, 31, 1, 92, 1, 11, 17, 64, 1, 61, 1, 24, 13, 59, 1, 156, 1, 13, 11, 16, 1, 71, 1, 176, 18, 43, 1, 124, 11, 3, 16, 4, 1, 123

Offset: 0

Author

Antti Karttunen, Feb 05 2022

Keywords

• nonn
• frac
• easy

Links

• Antti Karttunen, Table of n, a(n) for n = 0..65537
• Index entries for sequences related to primorial base

Crossrefs

Cf. A003415, A276086, A327858.

Cf. A351231 (denominators), A351232.

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); };
A351230(n) = numerator(A003415(n) / A276086(n));

Formula

a(n) = A003415(n) / A327858(n) = A003415(n) / gcd(A003415(n), A276086(n)).