A373146 a(n) = A276085(n) - A003415(n), where A003415 is the arithmetic derivative and A276085 is the primorial base log-function.

0, 0, 1, -2, 5, -2, 29, -9, -2, 0, 209, -12, 2309, 22, 0, -28, 30029, -16, 510509, -16, 22, 198, 9699689, -39, 2, 2296, -21, 0, 223092869, -22, 6469693229, -75, 198, 30012, 24, -54, 200560490129, 510490, 2296, -59, 7420738134809, -8, 304250263527209, 164, -29, 9699666, 13082761331670029, -106, 46, -32, 30012, 2256

Offset: 1

Author

Antti Karttunen, May 26 2024

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 1..2048

Crossrefs

Cf. A003415, A276085, A369650 (positions of 0's), A373145.

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)); };
A373146(n) = (A276085(n) - A003415(n));