A379967 Arithmetic derivative of {n divided by its largest squarefree divisor}: a(n) = A003415(A003557(n)).

0, 0, 0, 1, 0, 0, 0, 4, 1, 0, 0, 1, 0, 0, 0, 12, 0, 1, 0, 1, 0, 0, 0, 4, 1, 0, 6, 1, 0, 0, 0, 32, 0, 0, 0, 5, 0, 0, 0, 4, 0, 0, 0, 1, 1, 0, 0, 12, 1, 1, 0, 1, 0, 6, 0, 4, 0, 0, 0, 1, 0, 0, 1, 80, 0, 0, 0, 1, 0, 0, 0, 16, 0, 0, 1, 1, 0, 0, 0, 12, 27, 0, 0, 1, 0, 0, 0, 4, 0, 1, 0, 1, 0, 0, 0, 32, 0, 1, 1, 7, 0, 0, 0, 4

Offset: 1

Author

Antti Karttunen, Jan 22 2025

Keywords

• nonn

Links

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

Crossrefs

Cf. A003415, A003557.

Cf. also A028235, A341998, A342001.

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(factor(n)[, 1]));
A379967(n) = A003415(A003557(n));

Formula

a(n) = A003415(A003557(n)).