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