A258859 Ninth pi-based arithmetic derivative of n.

0, 0, 0, 0, 4, 0, 4, 4, 81920, 81920, 0, 0, 622592, 4, 512, 2304, 4931584, 4, 2304, 12288, 4931584, 512, 208, 12288, 193644, 12288, 2304, 8322048, 423168, 0, 81920, 0, 38944768, 12288, 0, 4, 37880, 81920, 4, 423168, 37880, 4, 80, 208, 2298880, 43632, 4, 512

Offset: 0

Author

Alois P. Heinz, Jun 12 2015

Keywords

• nonn

Links

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

Crossrefs

Column k=9 of A258850.

Cf. A000720, A258851.

Programs

Maple

with(numtheory):
d:= n-> n*add(i[2]*pi(i[1])/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..100);

Formula

a(n) = A258851^9(n).