A373147 a(n) = A003415(n) mod A276085(n), where A003415 is the arithmetic derivative and A276085 is the primorial base log-function.

0, 1, 0, 1, 2, 1, 0, 2, 0, 1, 0, 1, 9, 0, 0, 1, 1, 1, 0, 10, 13, 1, 4, 10, 15, 3, 0, 1, 4, 1, 0, 14, 19, 12, 0, 1, 21, 16, 5, 1, 8, 1, 48, 9, 25, 1, 4, 14, 6, 20, 56, 1, 4, 16, 26, 22, 31, 1, 2, 1, 33, 17, 0, 18, 61, 1, 72, 26, 22, 1, 2, 1, 39, 13, 80, 18, 71, 1, 6, 4, 43, 1, 22, 22, 45, 32, 140, 1, 2, 20, 96, 34, 49

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, A373148, and also A369971.

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)); };
A373147(n) = (A003415(n)%A276085(n));