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A294736
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Numbers that are the sum of 5 nonzero squares in exactly 2 ways.
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11
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20, 38, 41, 45, 47, 48, 49, 50, 54, 55, 63, 66, 81, 105
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OFFSET
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1,1
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COMMENTS
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Inspected values of n <= 50000.
This sequence is complete, see the von Eitzen Link and Price's computation that the next term must be > 50000. Proof. The link mentions "for positive integer n, if n > 5408 then the number of ways to write n as a sum of 5 squares is at least Floor(Sqrt(n - 101) / 8)". So for n > 5408, there are more than two ways to write n as a sum of 5 squares. For n <= 5408, it has been verified if n is in the sequence by inspection. Hence the sequence is complete." - David A. Corneth, Nov 08 2017
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REFERENCES
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E. Grosswald, Representations of Integers as Sums of Squares. Springer-Verlag, New York, 1985, p. 86, Theorem 1.
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LINKS
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FORMULA
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EXAMPLE
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There are exactly two ways 20 is a sum of 5 nonzero squares. These are 1^2 + 1^2 + 1^2 + 1^2 + 4^2 = 2^2 + 2^2 + 2^2 + 2^2 + 2^2 = 20. Therefore 20 is in the sequence.
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MATHEMATICA
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Select[Range[200], Length[Select[PowersRepresentations[#, 5, 2], #[[1]] > 0&]] == 2&] (* Jean-François Alcover, Nov 06 2020 *)
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CROSSREFS
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KEYWORD
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nonn,fini,full
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AUTHOR
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STATUS
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approved
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