A258854 Fourth pi-based arithmetic derivative of n.

0, 0, 0, 0, 4, 0, 4, 4, 80, 80, 2, 1, 208, 4, 12, 20, 512, 4, 20, 32, 512, 53, 30, 32, 324, 32, 16, 864, 704, 3, 80, 2, 2304, 32, 3, 7, 460, 80, 6, 704, 460, 4, 25, 8, 2432, 228, 7, 12, 6720, 332, 20, 56, 1188, 208, 3888, 116, 424, 32, 156, 4, 956, 12, 80, 764

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=4 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, 4):
seq(a(n), n=0..100);

Formula

a(n) = A258851^4(n).