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

0,5

Links

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

Formula

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

a(A258862(n)) = n.

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);

Crossrefs

Column k=2 of A258850.

Cf. A000720, A258851, A258862.

Sequence in context: A061469 A222641 A368437 * A021706 A224183 A131953

Adjacent sequences: A258849 A258850 A258851 * A258853 A258854 A258855

Keyword

nonn

Author

Alois P. Heinz, Jun 12 2015

Status

approved