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A047701
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All positive numbers that are not the sum of 5 nonzero squares.
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6
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1, 2, 3, 4, 6, 7, 9, 10, 12, 15, 18, 33
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listen;
history;
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internal format)
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OFFSET
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1,2
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REFERENCES
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J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 33, pp 12, Ellipses, Paris 2008.
E. Grosswald, Representations of Integers as Sums of Squares. Springer-Verlag, NY, 1985, Theorem 2., p. 73.
Ivan Niven and Herbert S. Zuckerman, An Introduction to the Theory of Numbers, New York: John Wiley (1980), p. 145
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LINKS
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EXAMPLE
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4 = 1^2 + 1^2 + 1^2 + 1^2 + 0^2, but the last square is 0, and hence 4 is in the sequence.
5 = 1^2 + 1^2 + 1^2 + 1^2 + 1^2, and therefore 5 is not in the sequence.
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MATHEMATICA
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Select[ Range[100], Select[ PowersRepresentations[#, 5, 2], FreeQ[#, 0]& ] == {}& ] (* Jean-François Alcover, Sep 03 2013 *)
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CROSSREFS
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KEYWORD
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nonn,full,fini
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AUTHOR
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Arlin Anderson (starship1(AT)gmail.com)
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EXTENSIONS
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STATUS
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approved
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