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A070073
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Number of distinct cuboids with integer sides <=n and cube-free volume.
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2
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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
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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LINKS
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_Reinhard Zumkeller_, Table of n, a(n) for n = 1..250
Eric Weisstein's World of Mathematics, cube-free numbers.
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EXAMPLE
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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.
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PROG
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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
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CROSSREFS
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Cf. A004709, A070072.
Cf. A212793.
Sequence in context: A182759 A022121 A171672 * A058565 A170901 A201882
Adjacent sequences: A070070 A070071 A070072 * A070074 A070075 A070076
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KEYWORD
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nonn
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AUTHOR
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Reinhard Zumkeller, Apr 21 2002
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STATUS
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approved
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