A070073 Number of distinct cuboids with integer sides <= n and cubefree volume.

1, 3, 8, 11, 23, 33, 57, 57, 70, 95, 142, 156, 220, 271, 338, 338, 441, 480, 609, 658, 775, 896, 1090, 1090, 1220, 1387, 1387, 1468, 1737, 1882, 2197, 2197, 2474, 2735, 3078, 3153, 3592, 3923, 4328, 4328, 4861, 5195, 5794

Offset: 1

Author

Reinhard Zumkeller, Apr 21 2002

Keywords

• nonn

Examples

			There are eleven cuboids with sides <= 4 having a cubefree volume: 1 X 1 X 1, 1 X 1 X 2, 1 X 1 X 3, 1 X 1 X 4, 1 X 2 X 2, 1 X 2 X 3, 1 X 3 X 3, 1 X 3 X 4, 2 X 2 X 3, 2 X 3 X 3 and 3 X 3 X 4 whereas 1 X 2 X 4, 1 X 4 X 4, 2 X 2 X 2, 2 X 2 X 4, 2 X 3 X 4, 2 X 4 X 4, 3 X 3 X 3 and 4 X 4 X 4 are not cubefree; therefore a(4)=11.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..250
• Eric Weisstein's World of Mathematics, Cubefree.

Crossrefs

Cf. A004709, A070072.

Cf. A212793.

Programs

Haskell

a070073 n = length [() | x <- [1..n], y <- [1..x], z <- [1..y],
                         a212793 (x*y*z) == 1]
-- Reinhard Zumkeller, May 27 2012