A373843 a(n) = gcd(n, A003415(A276085(n))), where A003415 is the arithmetic derivative and A276085 is the primorial base log-function.

1, 2, 1, 1, 5, 1, 1, 1, 1, 1, 1, 4, 1, 1, 3, 4, 1, 1, 19, 4, 1, 1, 1, 1, 1, 1, 1, 4, 1, 6, 1, 1, 3, 2, 5, 1, 1, 1, 1, 2, 1, 14, 1, 4, 1, 2, 47, 1, 1, 1, 1, 4, 1, 1, 5, 14, 1, 2, 1, 1, 1, 1, 1, 1, 5, 2, 1, 4, 1, 1, 1, 1, 1, 1, 3, 4, 1, 3, 79, 1, 3, 1, 1, 1, 5, 1, 1, 2, 1, 1, 1, 4, 1, 2, 1, 1, 1, 1, 1, 1, 1, 6, 1, 1, 21

Offset: 1

Author

Antti Karttunen, Jun 20 2024

Keywords

• nonn

Crossrefs

Cf. A003415, A276085, A373842.

Cf. also A327858 [= a(A276086(n))].

Programs

PARI

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A276085(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*prod(i=1,primepi(f[k, 1]-1),prime(i))); };
A373843(n) = gcd(n, A003415(A276085(n)));

Formula

a(n) = gcd(n, A373842(n)).