A356299 a(n) = gcd(A276086(n), A342001(n)), where A276086 is the primorial base exp-function, and A342001 is the arithmetic derivative without its inherited divisor.

2, 1, 1, 1, 1, 5, 1, 3, 2, 1, 1, 1, 1, 3, 2, 1, 1, 1, 1, 3, 10, 1, 1, 1, 2, 15, 3, 1, 1, 1, 1, 1, 14, 1, 6, 5, 1, 21, 2, 1, 1, 1, 1, 3, 1, 25, 1, 7, 2, 3, 10, 7, 1, 1, 2, 1, 2, 1, 1, 1, 1, 3, 1, 3, 18, 1, 1, 3, 2, 1, 1, 1, 1, 3, 1, 5, 18, 1, 1, 1, 2, 1, 1, 1, 2, 15, 2, 35, 1, 1, 2, 3, 2, 49, 6, 1, 1, 1, 5, 7, 1, 7, 1, 1, 1

Offset: 1

Author

Antti Karttunen, Nov 03 2022

Keywords

• nonn

Comments

Each term a(n) is a factor of A327858(n).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences related to primorial base

Crossrefs

Cf. A003415, A003557, A046337 (positions of even terms), A276086, A342001, A327858.

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]));
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A342001(n) = (A003415(n) / A003557(n));
A356299(n) = gcd(A276086(n), A342001(n));