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A291850
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Numbers k such that k^2 is the sum of two positive 5th powers.
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0
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8, 256, 1944, 6655, 8192, 25000, 35937, 62208, 134456, 212960, 262144, 344605, 453962, 472392, 692759, 800000, 1149984, 1288408, 1617165, 1990656, 2970344, 4302592, 6075000, 6814720, 8388608, 8732691, 11358856, 14526784, 15116544, 19808792, 20796875, 22168288
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OFFSET
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1,1
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COMMENTS
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If a^5 + b^5 = m, then (ma)^5 + (mb)^5 = m^6 = (m^3)^2 is square. Therefore A003347(n)^3 are terms of this sequence.
When k in this sequence, k * (n^5) (n = 2, 3, ... ) is also in this sequence.
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LINKS
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EXAMPLE
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8^2 = 2^5 + 2^5, so 8 is in the sequence.
6655^2 = 22^5 + 33^5, so 6655 is in the sequence.
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MATHEMATICA
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lst={}; Do[If[IntegerQ[(n^2-a^5)^(1/5)], AppendTo[lst, n^2]], {n, 7000}, {a, n^2/2)^(1/5)}]; lst
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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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