A258852 Second pi-based arithmetic derivative of n.

0, 0, 0, 1, 4, 2, 4, 4, 20, 20, 5, 3, 32, 7, 19, 8, 80, 4, 37, 12, 80, 25, 26, 12, 76, 53, 30, 135, 64, 11, 16, 5, 208, 12, 11, 13, 188, 20, 41, 64, 188, 6, 21, 15, 192, 88, 13, 19, 448, 116, 86, 58, 108, 32, 351, 49, 156, 53, 56, 7, 260, 33, 16, 332, 704, 73

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=2 of A258850.

Cf. A000720, A258851, A258862.

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..100);

Formula

a(n) = A258851^2(n).

a(A258862(n)) = n.