A258650 Tenth arithmetic derivative of n.

0, 0, 0, 0, 4, 0, 0, 0, 8592, 0, 0, 0, 20096, 0, 0, 3424, 70464, 0, 0, 0, 16304, 0, 0, 0, 32624, 0, 1520, 27, 70464, 0, 0, 0, 235072, 0, 0, 8592, 47872, 0, 0, 20096, 24640, 0, 0, 0, 65264, 8592, 0, 0, 130544, 0, 3424, 8144, 47872, 0, 57996, 20096, 198656, 0, 0

Offset

0,5

Links

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

Formula

a(n) = A003415^10(n).

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, 10):
seq(a(n), n=0..70);

Prog

(Python)
from sympy import factorint
def A258650(n):
    for _ in range(10):
        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

Crossrefs

Column k=10 of A258651.

Cf. A003415.

Sequence in context: A258648 A185232 A258649 * A156393 A335510 A331438

Adjacent sequences: A258647 A258648 A258649 * A258651 A258652 A258653

Keyword

nonn

Author

Alois P. Heinz, Jun 06 2015

Status

approved