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

1,1

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

Links

Table of n, a(n) for n=1..22.

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]]

Crossrefs

Cf. A207638, A207639.

Sequence in context: A359598 A207639 A077347 * A267892 A363217 A373087

Adjacent sequences: A207637 A207638 A207639 * A207641 A207642 A207643

Keyword

nonn,more

Author

Vladimir Joseph Stephan Orlovsky, Feb 19 2012

Extensions

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

Status

approved