A369449 a(n) = A003415(gcd(A003415(n), A276086(n))), where A003415 is the arithmetic derivative and A276086 is the primorial base exp-function.

0, 1, 0, 0, 0, 0, 1, 0, 1, 5, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 7, 0, 0, 0, 7, 8, 1, 0, 0, 0, 0, 0, 9, 0, 5, 1, 0, 10, 1, 0, 0, 0, 0, 1, 1, 10, 0, 1, 9, 8, 7, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 21, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 21, 0, 0, 0, 5, 0, 0, 0, 1, 8, 1, 12, 0, 0, 1, 1, 1, 14, 5, 0, 0, 1, 8, 12, 0, 1

Offset: 0

Author

Antti Karttunen, Jan 26 2024

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 0..16384

Crossrefs

Cf. A003415, A276086, A327858.

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); };
A369449(n) = A003415(gcd(A003415(n), A276086(n)));

Formula

a(n) = A003415(A327858(n)).