A013941 a(n) = Sum_{k = 1..n} floor(n/prime(k)^3).

0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11

Offset: 1

Author

N. J. A. Sloane, Henri Lifchitz

Keywords

• nonn
• easy

Crossrefs

Cf. A013940.

Partial sums of A295659.

Programs

Maple

A013941:=n->add(floor(n/ithprime(k)^3), k=1..n): seq(A013941(n), n=1..150); # Wesley Ivan Hurt, Jan 29 2017

Mathematica

Table[Floor[Sum[n/Prime[k]^3, {k, n}]], {n, 75}] (* Alonso del Arte, Jan 29 2017 *)

PARI

a(n) = sum(k = 1, n, n\prime(k)^3); \\ Michel Marcus, Aug 24 2013

Formula

G.f.: (1/(1 - x))*Sum_{k>=1} x^(prime(k)^3)/(1 - x^(prime(k)^3)). - Ilya Gutkovskiy, Feb 11 2017