A369971 a(n) = A003415(n) mod A276086(n), where A003415 is the arithmetic derivative, and A276086 is the primorial base exp-function.

0, 0, 1, 1, 4, 1, 0, 1, 12, 6, 7, 1, 16, 1, 9, 8, 32, 1, 21, 1, 24, 10, 13, 1, 44, 10, 15, 27, 32, 1, 3, 1, 17, 14, 19, 12, 25, 1, 21, 16, 68, 1, 41, 1, 48, 39, 25, 1, 112, 14, 45, 20, 56, 1, 81, 16, 92, 22, 31, 1, 43, 1, 33, 51, 192, 18, 61, 1, 72, 26, 59, 1, 156, 1, 39, 55, 80, 18, 71, 1, 176, 108, 43, 1, 124, 22

Offset: 0

Author

Antti Karttunen, Feb 07 2024

Keywords

• nonn

Links

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

Crossrefs

Cf. A003415, A276086, A369970 (positions of 0's).

Cf. also A327858 [= gcd(a(n), A276086(n))], A328382, A342014.

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); };
A369971(n) = (A003415(n)%A276086(n));