A013938 a(n) = Sum_{k=1..n} floor(n/k^4).

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 85, 87

Offset: 1

Author

N. J. A. Sloane, Henri Lifchitz

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A013936, A013937.

Programs

Mathematica

Table[Sum[Floor[n/k^4], {k, 1, n}], {n, 1, 100}] (* Vaclav Kotesovec, Oct 12 2019 *)

PARI

a(n) = sum(k=1, n, n\k^4); \\ Michel Marcus, Feb 11 2017

Formula

G.f.: (1/(1 - x))*Sum_{k>=1} x^(k^4)/(1 - x^(k^4)). - Ilya Gutkovskiy, Feb 11 2017

a(n) ~ zeta(4)*n = Pi^4*n/90. - Vaclav Kotesovec, Oct 12 2019