A373148 a(n) = A276085(n) mod A003415(n), where A003415 is the arithmetic derivative and A276085 is the primorial base log-function.

0, 0, 2, 0, 3, 0, 3, 4, 0, 0, 4, 0, 4, 0, 4, 0, 5, 0, 8, 2, 3, 0, 5, 2, 1, 6, 0, 0, 9, 0, 5, 2, 11, 0, 6, 0, 1, 8, 9, 0, 33, 0, 20, 10, 16, 0, 6, 4, 13, 12, 16, 0, 7, 8, 33, 2, 7, 0, 10, 0, 1, 34, 6, 12, 30, 0, 8, 2, 37, 0, 7, 0, 1, 14, 32, 6, 41, 0, 10, 8, 31, 0, 34, 6, 16, 8, 73, 0, 11, 0, 44, 2, 36, 12, 7, 0, 61

Offset: 2

Author

Antti Karttunen, May 27 2024

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 2..65537

Crossrefs

Cf. A002110, A003415, A276085.

Cf. also A373145, A373147, and also A328382.

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)); };
A373148(n) = (A276085(n)%A003415(n));