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 A280991 Positive integers that can be expressed as the sum of four pairwise coprime squares. 2
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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 REFERENCES R. K. Guy, Unsolved Problems in Theory of Numbers, Section C20 LINKS Jean-François Alcover, Table of n, a(n) for n = 1..1000 EXAMPLE 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. MATHEMATICA 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]&] CROSSREFS Sequence in context: A051215 A192112 A034885 * A256726 A130324 A020677 Adjacent sequences:  A280988 A280989 A280990 * A280992 A280993 A280994 KEYWORD nonn AUTHOR Emmanuel Vantieghem, Jan 12 2017 STATUS approved

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Last modified September 27 08:39 EDT 2021. Contains 347689 sequences. (Running on oeis4.)