A207640 Squares that can be written as a sum of 3 distinct nonzero squares in exactly two ways.

225, 361, 625, 900, 1444, 2500, 3600, 5776, 10000, 14400, 23104, 40000, 57600, 92416, 160000, 230400, 369664, 640000, 921600, 1478656, 2560000, 3686400

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Feb 19 2012

Keywords

• nonn
• more

Comments

k is a term if and only if 4*k is a term. Are 225, 361 and 625 the only terms not divisible by 4? - Robert Israel, Jan 28 2025

Crossrefs

Cf. A207638, A207639.

Programs

Maple

N:= 1000; # for squares up to N^2
V:= Vector(N):
for x from 1 to N-1 do
  for y from 1 to x-1 while x^2 + y^2 < N^2 do
    for z from 1 to y-1 do
      s:= x^2 + y^2 + z^2;
      if s > N^2 then break fi;
      if issqr(s) then
        v:= sqrt(s);
        V[v]:= V[v]+1
      fi
od od od:
map(`^`, select(t -> V[t]=2, [$1..N]),2); # Robert Israel, Jan 28 2025

Mathematica

t = Sort[Select[Flatten[Table[x^2 + y^2 + z^2, {x, 400}, {y, x + 1, 400}, {z, y + 1, 400}]], # < 160006 && IntegerQ[Sqrt[#]] &]];
f1[l_] := Module[{t = {}}, Do[If[l[[n]] != l[[n + 1]] && l[[n]] != l[[n - 1]], AppendTo[t, l[[n]]]], {n, Length[l] - 1}]; t];
f2[l_] := Module[{t = {}}, Do[If[l[[n]] == l[[n + 1]], AppendTo[t, l[[n]]]], {n, Length[l] - 1}]; t];
s1 = Join[{First[t]}, f1[t]];
Complement[t, s1];
t = f2[t];
s2 = Join[{First[t]}, f1[t]]

Extensions

a(15)-a(22) from Robert Israel, Jan 28 2025