

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
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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

JeanFrançois 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



