A280991 Positive integers that can be expressed as the sum of four pairwise coprime squares.

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

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