A258849 The n-th pi-based arithmetic derivative of n.

0, 0, 0, 0, 4, 0, 4, 4, 12288, 81920, 0, 0, 278380544, 4, 4931584, 278380544, 14768867966976, 4, 128412352512, 14768867966976, 375877192068366336, 14768867966976, 14768867966976, 375877192068366336

Offset: 0

Author

Alois P. Heinz, Jun 12 2015

Keywords

• nonn

Crossrefs

Main diagonal 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$2):
seq(a(n), n=0..23);

Formula

a(n) = A258851^n(n) = A258850(n,n).