A258864 Partial sums of the pi-based arithmetic derivative sequence A258851.

0, 0, 1, 3, 7, 10, 17, 21, 33, 45, 56, 61, 81, 87, 102, 121, 153, 160, 193, 201, 233, 259, 280, 289, 341, 371, 396, 450, 494, 504, 557, 568, 648, 685, 716, 757, 841, 853, 888, 932, 1016, 1029, 1102, 1116, 1180, 1267, 1308, 1323, 1451, 1507, 1592, 1647, 1723

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

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) option remember; d(n)+`if`(n>0, a(n-1), 0) end:
seq(a(n), n=0..100);

Formula

a(n) = Sum_{k=0..n} A258851(k).