A373145 a(n) = gcd(A003415(n), A276085(n)), where A003415 is the arithmetic derivative and A276085 is the primorial base log-function.

0, 1, 1, 2, 1, 1, 1, 3, 2, 7, 1, 4, 1, 1, 8, 4, 1, 1, 1, 8, 2, 1, 1, 1, 2, 1, 3, 32, 1, 1, 1, 5, 2, 1, 12, 6, 1, 1, 8, 1, 1, 1, 1, 4, 1, 1, 1, 2, 2, 1, 4, 8, 1, 1, 8, 1, 2, 1, 1, 2, 1, 1, 17, 6, 6, 1, 1, 8, 2, 1, 1, 1, 1, 1, 1, 16, 6, 1, 1, 2, 4, 1, 1, 2, 2, 1, 8, 1, 1, 1, 20, 4, 2, 1, 12, 1, 1, 1, 1, 14, 1, 1, 1, 1, 1

Offset: 1

Author

Antti Karttunen, May 26 2024

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A003415, A276086, A373146, A373147, A373148.

Cf. A368998 (positions of even terms), A368999 (of odd terms), A373144 (of multiples of 3).

Cf. also A327858.

Programs

PARI

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A002110(n) = prod(i=1,n,prime(i));
A276085(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*A002110(primepi(f[k, 1])-1)); };
A373145(n) = gcd(A003415(n), A276085(n));

Formula

a(n) = gcd(A003415(n), A373146(n)) = gcd(A276085(n), A373146(n)).

For n > 1, a(n) = gcd(A276085(n), A373147(n)) = gcd(A003415(n), A373148(n)).