A258853 Third pi-based arithmetic derivative of n.

0, 0, 0, 0, 4, 1, 4, 4, 32, 32, 3, 2, 80, 4, 8, 12, 208, 4, 12, 20, 208, 30, 25, 20, 108, 16, 53, 351, 192, 5, 32, 3, 512, 20, 5, 6, 248, 32, 13, 192, 248, 7, 26, 19, 704, 172, 6, 8, 1600, 156, 71, 49, 324, 80, 864, 56, 332, 16, 116, 4, 536, 37, 32, 424, 2432

Offset: 0

Author

Alois P. Heinz, Jun 12 2015

Keywords

• nonn
• look

Links

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

Crossrefs

Column k=3 of A258850.

Cf. A000720, A258851, A258995.

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, 3):
seq(a(n), n=0..100);

Formula

a(n) = A258851^3(n).

a(A258995(n)) = n.