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A091414
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Least number that is the sum of n positive n-th powers in at least 2 ways.
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2
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50, 251, 259, 4097, 570947, 73310705, 647282661, 79327628290, 1077347903894, 1761813250036143, 2343908545594901
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OFFSET
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2,1
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COMMENTS
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a(11) = 2^11 + 2^11 + 2^11 + 2^11 + 8^11 + 10^11 + 10^11 + 15^11 + 22^11 + 22^11 + 22^11 = 3^11 + 5^11 + 5^11 + 5^11 + 6^11 + 9^11 + 11^11 + 12^11 + 17^11 + 20^11 + 24^11.
a(12) = 2^12 + 2^12 + 2^12 + 2^12 + 2^12 + 2^12 + 2^12 + 9^12 + 9^12 + 9^12 + 15^12 + 19^12 = 3^12 + 5^12 + 5^12 + 10^12 + 10^12 + 10^12 + 10^12 + 12^12 + 12^12 + 17^12 + 17^12 + 18^12.
a(13) > 876*10^15. a(14) > 799*10^15. a(15) > 115*10^16. (End)
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LINKS
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FORMULA
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a(n) <= A230477(n) for n > 1, with equality at least for n = 2 and inequality at least for n = 3, 4, 5. - Jonathan Sondow, Oct 24 2013
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EXAMPLE
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a(3) = 251 because 251 = 1^3 + 5^3 + 5^3 = 2^3 + 3^3 + 6^3 and it is the smallest number that can be represented two ways as the sum of three third powers.
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CROSSREFS
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KEYWORD
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more,nonn
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AUTHOR
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Gabriel Cunningham (gcasey(AT)mit.edu), Mar 02 2004
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EXTENSIONS
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STATUS
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approved
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