A025339 Numbers that are the sum of 3 distinct nonzero squares in exactly one way.

14, 21, 26, 29, 30, 35, 38, 41, 42, 45, 46, 49, 50, 53, 54, 56, 59, 61, 65, 66, 70, 75, 78, 81, 83, 84, 91, 93, 104, 106, 107, 109, 113, 114, 115, 116, 118, 120, 121, 133, 137, 139, 140, 142, 145, 147, 152, 153, 157, 162, 164, 168, 169, 171, 178, 180, 184, 190, 196, 198, 200

Offset

1,1

Comments

Numbers n such that there is a unique triple (i,j,k) with 0 < i < j < k and n = i^2 + j^2 + k^2.

By removing the terms that have a factor of 4 we obtain A096017. - T. D. Noe, Jun 15 2004

Links

Robert Israel, Table of n, a(n) for n = 1..1019

Index entries for sequences related to sums of squares

Example

14 is a term since 14 = 1^2+2^2+3^2.
38 is a term since 38 = 2^2+3^2+5^2 (note that 38 is also 1^2+1^2+6^2, but that is not a contradiction since here i=j).

Maple

N:= 10^4; # to get all terms <= N
S:= Vector(N):
for a from 1 to floor(sqrt(N/3)) do
  for b from a+1 to floor(sqrt((N-a^2)/2)) do
    c:= [$(b+1) .. floor(sqrt(N-a^2-b^2))]:
    v:= map(t -> a^2 + b^2 + t^2, c):
    S[v]:= map(`+`, S[v], 1)
od od:
select(t -> S[t]=1, [$1..N]); # Robert Israel, Jan 03 2016

Mathematica

Select[Range[200], (pr = PowersRepresentations[#, 3, 2]; Length[Select[pr, Union[#] == # && #[[1]] > 0&]] == 1)&] (* Jean-François Alcover, Feb 27 2019 *)

Crossrefs

A subsequence of A004432.

Cf. A001974, A024803, A096017.

A274226 has a somewhat similar definition but is actually a different sequence.

Sequence in context: A001944 A024803 A004432 * A224771 A096017 A274226

Adjacent sequences: A025336 A025337 A025338 * A025340 A025341 A025342

Keyword

nonn

Author

David W. Wilson

Status

approved