A369009 a(n) = A342001(n) - A083345(n).

0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 2, 8, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 7, 0, 0, 0, 14, 0, 6, 0, 0, 0, 0, 0, 23, 0, 0, 0, 3, 0, 0, 0, 18, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, 11, 0, 0, 0, 31, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 10

Offset: 1

Author

Antti Karttunen, Jan 14 2024

Keywords

• nonn

Comments

Arithmetic derivative of n without its "inherited divisor" minus the arithmetic derivative of n without its greatest common divisor with n.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..100000

Crossrefs

Cf. A003415, A003557, A083345, A085731, A342001, A369008.

Cf. A342090 (positions of terms > 0).

Programs

PARI

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A003557(n) = (n/factorback(factorint(n)[, 1]));
A369009(n) = { my(u=A003415(n)); (u/A003557(n))-(u/gcd(n,u)); };