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Search: id:A014544
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| A014544 |
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Numbers n such that a cube can be divided into n sub-cubes. |
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+0
3
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| 1, 8, 15, 20, 22, 27, 29, 34, 36, 38, 39, 41, 43, 45, 46, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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If m and n are in the sequence, so is m+n-1, since n-dissecting one cube in an m-dissection gives an (m+n-1)-dissection. 1, 8, 20, 38, 49, 51, 54 are in the sequence because of dissections corresponding to the equations 1^3=1^3, 2^3=8*1^3, 3^3=2^3+19*1^3, 4^3=3^3+37*1^3, 6^3=4*3^3+9*2^3+36*1^3, 6^3=5*3^3+5*2^3+41*1^3, and 8^3=6*4^3+2*3^3+4*2^3+42*1^3.
Combining these facts gives the remaining terms shown, and all numbers > 47.
It may or may not have been shown that no other numbers occur - see Hickerson link.
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REFERENCES
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J.-P. Delahaye, Les inattendus mathematiques, pp. 93 Belin-Pour la science, Paris, 2004.
Eves, Howard, A Survey of Geometry, Vol. 1. Allyn and Bacon, Inc., Boston, Mass. 1966, see p. 271.
M. Gardner, Fractal Music, Hypercards and More: Mathematical Recreations from Scientific American Magazine. New York: W. H. Freeman, pp. 297-298, 1992.
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LINKS
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Dean Hickerson, Further comments on A014544, Nov 01 2007 and Nov 10 2007
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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CROSSREFS
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Adjacent sequences: A014541 A014542 A014543 this_sequence A014545 A014546 A014547
Sequence in context: A114605 A031103 A133157 this_sequence A122754 A082867 A075713
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KEYWORD
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easy,nonn
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AUTHOR
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Eric Weisstein (eric(AT)weisstein.com)
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EXTENSIONS
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More terms from Jud McCranie (j.mccranie(AT)comcast.net), Mar 19 2001, who remarks that all integers > 47 are in the sequence.
Edited by Dean Hickerson (dean(AT)math.ucdavis.edu), Jan 05 2003
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