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A066215
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Numbers which are sums of cubes of some subset of divisors.
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4
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1, 8, 27, 36, 64, 72, 125, 216, 252, 288, 343, 378, 512, 520, 576, 584, 729, 738, 756, 792, 828, 855, 954, 972, 1000, 1044, 1331, 1350, 1440, 1520, 1540, 1728, 1764, 1800, 1890, 1944, 1980, 2016, 2070, 2160, 2197, 2304, 2352, 2376, 2400, 2484, 2520, 2548
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OFFSET
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1,2
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COMMENTS
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There are cubes that have not a single, trivial representation but more than one. These start with 27000 =+8^3+9^3+10^3+12^3+15^3+18^3+24^3 =+1^3+2^3+4^3+6^3+8^3+10^3+15^3+20^3+24^3 = +2^3+4^3+9^3+10^3+15^3+20^3+24^3 =+1^3+2^3+4^3+12^3+15^3+20^3+24^3 =+2^3+3^3+4^3+5^3+6^3+12^3+15^3+18^3+25^3 =+1^3+4^3+5^3+6^3+8^3+9^3+12^3+20^3+25^3 =+15^3+20^3+25^3 = +1^3+3^3+6^3+8^3+9^3+18^3+27^3 =+30^3 and 46656 =+1^3+2^3+3^3+6^3+8^3+9^3+12^3+16^3+18^3+24^3+27^3 =+4^3+24^3+32^3 =+36^3 and 74088 =+2^3+6^3+7^3+8^3+9^3+12^3+18^3+21^3+24^3+27^3+28^3 =+4^3+6^3+8^3+14^3+18^3+21^3+24^3+27^3+28^3 =+42^3. - R. J. Mathar, Jan 21 2024
If m is in the sequence then so is m*k^3 for k >= 1. - David A. Corneth, Jan 21 2024
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LINKS
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EXAMPLE
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72 is in the list since 72 = 2^3 + 4^3 and 2 and 4 are divisors of 72
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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