login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A280991 Positive integers that can be expressed as the sum of four pairwise coprime squares. 1
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-Fran├žois 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 20 17:09 EST 2019. Contains 329337 sequences. (Running on oeis4.)