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A281789
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Numbers n such that n^3-1 is a sum of cubes in 1 way and a difference of cubes in 2 ways.
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1
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9, 144, 577, 729, 1010, 2304, 3097, 3753, 5625, 11664, 21609, 36864, 51762, 59049, 90000, 131769, 186624, 243876, 257049, 345744, 455625, 589824, 713337, 751689, 826809, 944784, 1172889, 1440000, 1613673, 1750329, 2108304, 2518569, 2985984, 3132585, 3515625
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OFFSET
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1,1
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COMMENTS
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By Fermat's Last Theorem, n^3 cannot be the difference nor the sum of 2 positive cubes, but n^3+1 or n^3-1 could be. If n^3-1 is also the sum of positive cubes and the difference of two other positives cubes besides n^3 and 1^3, then n is a term of the sequence. Interestingly, I have not been able to find numbers n such that n^3+1 is a difference of 2 positive cubes in 1 way and the sum of 2 positive cubes in 2 ways.
Conjecture: if a term n is square, then 10000*n is also a term.
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LINKS
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EXAMPLE
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3515625 is a term since 3515625^3 - 1 = 140624^3 + 3515550^3 = 3515700^3 - 140626^3.
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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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