A258847 Sum of the k-th pi-based arithmetic derivative of n-k for k=0..n.

0, 1, 2, 4, 6, 10, 13, 20, 21, 33, 54, 86, 146, 339, 788, 2947, 14870, 94801, 706961, 5566784, 43958933, 317950465, 2406052444, 19645433193, 146175038733, 1479263447899, 16135114175706, 203382520812382, 2606355260220040, 32974597626726301, 406609097787758227

Offset: 0

Author

Alois P. Heinz, Jun 12 2015

Keywords

• nonn

Crossrefs

Antidiagonal sums of A258850.

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, k) option remember; `if`(k=0, n, d(A(n, k-1))) end:
a:= proc(n) option remember; add(A(h, n-h), h=0..n) end:
seq(a(n), n=0..30);

Formula

a(n) = Sum_{k=0..n} A258850(n-k,k).