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A280991
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Positive integers that can be expressed as the sum of four pairwise coprime squares.
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2
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3, 4, 7, 12, 15, 19, 27, 28, 31, 36, 39, 43, 51, 52, 55, 60, 63, 67, 75, 76, 79, 84, 87, 91, 99, 103, 108, 111, 115, 123, 124, 127, 132, 135, 139, 147, 148, 151, 156, 159, 163, 171, 172, 175, 180, 183, 187, 195, 196, 199, 204, 207, 211, 219, 220, 223, 228, 231, 235, 243, 244, 247
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OFFSET
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1,1
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COMMENTS
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If n is in the sequence, then n == 0 or 1 mod 3 and n == 3, 4, or 7 mod 8. But the converse is not true: 100 and 268 are not in the sequence (are there other examples?).
Guy [op. cit.] quotes Paul Turan as asking for a characterization of the terms of this sequence. - N. J. A. Sloane, Jan 16 2017
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REFERENCES
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R. K. Guy, Unsolved Problems in Theory of Numbers, Section C20
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LINKS
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EXAMPLE
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3 is in the sequence, since 3 is the sum of the squares of 0, 1, 1, 1 and these four numbers are pairwise coprime.
7 is in the sequence, since 7 is the sum of the squares of 1, 1, 1, 2 and these four numbers are pairwise coprime.
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MATHEMATICA
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f[A_]:=Module[{A2, La2}, A2=Subsets[A, {2}]; La2=Length[A2]; Union[Table[GCD@@A2[[i]], {i, 1, La2}]]=={1}];
Select[Range[250], MemberQ[Union[f/@PowersRepresentations[#, 4, 2]], True]&]
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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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