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

0,5

Links

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

Formula

a(n) = A258851^4(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, 4):
seq(a(n), n=0..100);

Crossrefs

Column k=4 of A258850.

Cf. A000720, A258851.

Sequence in context: A110854 A278086 A021716 * A258855 A258856 A258857

Adjacent sequences: A258851 A258852 A258853 * A258855 A258856 A258857

Keyword

nonn

Author

Alois P. Heinz, Jun 12 2015

Status

approved