A258649 Ninth arithmetic derivative of n.

0, 0, 0, 0, 4, 0, 0, 0, 3424, 0, 0, 0, 8592, 0, 0, 1520, 20096, 0, 0, 0, 8144, 0, 0, 0, 16304, 0, 752, 27, 20096, 0, 0, 0, 70464, 0, 0, 3424, 22288, 0, 0, 8592, 7744, 0, 0, 0, 32624, 3424, 0, 0, 65264, 0, 1520, 3120, 22288, 0, 23112, 8592, 47872, 0, 0, 0, 47872

Offset: 0

Author

Alois P. Heinz, Jun 06 2015

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000

Crossrefs

Column k=9 of A258651.

Cf. A003415.

Programs

Maple

d:= n-> n*add(i[2]/i[1], i=ifactors(n)[2]):
A:= proc(n, k) option remember; `if`(k=0, n, d(A(n, k-1))) end:
a:= n-> A(n, 9):
seq(a(n), n=0..70);

Python

from sympy import factorint
def A258649(n):
    for _ in range(9):
        if n <= 1: return 0
        n = sum((n*e//p for p,e in factorint(n).items()))
    return n # Chai Wah Wu, Nov 03 2022

Formula

a(n) = A003415^9(n).