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A070073 Number of distinct cuboids with integer sides <=n and cube-free volume. 2

%I

%S 1,3,8,11,23,33,57,57,70,95,142,156,220,271,338,338,441,480,609,658,

%T 775,896,1090,1090,1220,1387,1387,1468,1737,1882,2197,2197,2474,2735,

%U 3078,3153,3592,3923,4328,4328,4861,5195,5794

%N Number of distinct cuboids with integer sides <=n and cube-free volume.

%H Reinhard Zumkeller, <a href="/A070073/b070073.txt">Table of n, a(n) for n = 1..250</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Cubefree.html">cube-free numbers</a>.

%e There are eleven cuboids with sides <=4 having a cube-free 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 cube-free; therefore a(4)=11.

%o (Haskell)

%o a070073 n = length [() | x <- [1..n], y <- [1..x], z <- [1..y],

%o a212793 (x*y*z) == 1]

%o -- _Reinhard Zumkeller_, May 27 2012

%Y Cf. A004709, A070072.

%Y Cf. A212793.

%K nonn

%O 1,2

%A _Reinhard Zumkeller_, Apr 21 2002

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Last modified September 30 23:47 EDT 2014. Contains 247496 sequences.