A079631 Number of k less than or equal to n such that floor(k^(1/3)) divides k.

1, 2, 3, 4, 5, 6, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 18, 18, 18, 19, 19, 19, 20, 20, 20, 21, 21, 21, 22, 22, 22, 23, 23, 23, 24, 24, 24, 25, 25, 25, 26, 26, 26, 27, 27, 27, 28, 28, 28, 29, 29, 29, 30, 31, 31, 31, 31, 32, 32, 32, 32, 33, 33

Offset: 1

Author

Benoit Cloitre, Jan 30 2003

Keywords

• nonn

Comments

Concrete Mathematics Casino Problem - number of winners up to N.

Examples

			a(1000)=172
		

References

• R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. 2nd Edition. Addison-Wesley, Reading, MA, 1994. Section 3.2, p74-76.

Links

• Hugo Pfoertner, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A321667.

Programs

Mathematica

Accumulate[Boole[Table[IntegerQ[n/Floor[n^(1/3)]], {n, 1, 73}]]] (* Geoffrey Critzer, May 25 2013 *)

Formula

a(n)=floor(n/floor(n^(1/3)))+1/2*floor(n^(1/3))^2+5/2*floor(n^(1/3))-3