%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 cubefree 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">cubefree numbers</a>.
%e 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.
%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
