A207638 -id:A207638 - cp's OEIS frontend

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

Vladimir Joseph Stephan Orlovsky, Feb 19 2012

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

Cf. A207638, A207639.

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

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]]

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

A207650 Squares that can be written as a sum of 3 distinct nonzero squares in 3 or more ways.

Original entry on oeis.org

441, 529, 729, 841, 961, 1089, 1225, 1369, 1521, 1681, 1764, 1849, 2025, 2116, 2209, 2401, 2601, 2809, 2916, 3025, 3249, 3364, 3481, 3721, 3844, 3969, 4225, 4356, 4489, 4761, 4900, 5041, 5329, 5476, 5625, 5929, 6084, 6241, 6561, 6724, 6889, 7056, 7225, 7396

Offset: 1

Vladimir Joseph Stephan Orlovsky, Feb 19 2012

nonn

Cf. A161992, A206606, A207638, A207639, A207640.

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]];
Complement[t, s2]

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

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