A369964 a(n) = gcd(n, A276086(A003415(n))), where A003415 is the arithmetic derivative, and A276086 is the primorial base exp-function.

1, 1, 2, 1, 1, 1, 6, 1, 1, 1, 10, 1, 3, 1, 2, 15, 1, 1, 6, 1, 5, 3, 2, 1, 3, 5, 2, 3, 7, 1, 2, 1, 1, 3, 2, 5, 1, 1, 2, 3, 5, 1, 42, 1, 1, 15, 2, 1, 3, 1, 50, 3, 1, 1, 6, 5, 7, 3, 2, 1, 3, 1, 2, 21, 1, 5, 2, 1, 1, 3, 70, 1, 1, 1, 2, 25, 1, 1, 6, 1, 5, 1, 2, 1, 21, 5, 2, 3, 1, 1, 6, 1, 1, 3, 2, 5, 3, 1, 98, 3, 25

Offset: 0

Author

Antti Karttunen, Feb 11 2024

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 0..65537

Crossrefs

Cf. A003415, A276086, A327859, A370114 (fixed points, see also A369650), A370116, A370117.

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); };
A369964(n) = gcd(n, A276086(A003415(n)));

Formula

a(n) = gcd(n, A327859(n)) = gcd(n, A276086(A003415(n))).

For n >= 1, a(n) = n / A370116(n).

For n >= 0, a(n) = A327859(n) / A370117(n).