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A078129
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Numbers which cannot be written as sum of cubes>1.
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5
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1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 25, 26, 28, 29, 30, 31, 33, 34, 36, 37, 38, 39, 41, 42, 44, 45, 46, 47, 49, 50, 52, 53, 55, 57, 58, 60, 61, 63, 65, 66, 68, 69, 71, 73, 74, 76, 77, 79, 82, 84, 85, 87, 90, 92, 93, 95, 98, 100, 101, 103, 106, 109, 111, 114, 117, 119, 122
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| A078128(a(n))=0.
The sequence is finite because every number greater than 181 can be represented using just 8 and 27. - Frank Adams-Watters (FrankTAW(AT)Netscape.net), Apr 21 2006
Contribution from Benoit Jubin (benoit_jubin(AT)yahoo.fr), Jun 29 2010: More generally, the numbers which are not the sum of k^th powers larger than 1 are exactly those in [1,6^k-3^k-2^k] but not of the form 2^k.a+3^k.b+5^k.c with a,b,c nonnegative. This relies on the following fact applied to m=2^k and n=3^k: if m and n are relatively prime, then the largest number which is not a linear combination of m and n with positive integer coefficients is mn-m-n. (End)
The complete list is 1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 25, 26, 28, 29, 30, 31, 33, 34, 36, 37, 38, 39, 41, 42, 44, 45, 46, 47, 49, 50, 52, 53, 55, 57, 58, 60, 61, 63, 65, 66, 68, 69, 71, 73, 74, 76, 77, 79, 82, 84, 85, 87, 90, 92, 93, 95, 98, 100, 101, 103, 106, 109, 111, 114, 117, 119, 122, 127, 130, 138, 146, 154. - Benoit Jubin (benoit_jubin(AT)yahoo.fr), Jun 29 2010
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LINKS
| Eric Weisstein's World of Mathematics, Cubic Number.
Index entries for sequences related to sums of cubes
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EXAMPLE
| 181 is not in the list since 181 = 7*2^3 + 5^3.
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CROSSREFS
| Cf. A000578, A078131, A078133, A078130, A078135.
Sequence in context: A007915 A004709 A048107 * A188437 A003796 A032896
Adjacent sequences: A078126 A078127 A078128 * A078130 A078131 A078132
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KEYWORD
| nonn,fini,full
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AUTHOR
| Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 19 2002
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EXTENSIONS
| Sequence completed by Frank Adams-Watters (FrankTAW(AT)Netscape.net), Apr 21 2006
Edited by R. J. Mathar and N. J. A. Sloane, Jul 06 2010
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