

One form of   Pythagorean quadruples   is   (for positive integers   a,   b,   c,   and   d):



    a2   +   b2   +   c2     =     d2 


An example:

    22   +   32   +   62     =     72 
 which is:
    4    +   9    +   36     =     49 


Task

For positive integers up   2,200   (inclusive),   for all values of   a,  
b,   c,   and   d,

find   (and show here)   those values of   d   that   can't   be represented.

Show the values of   d   on one line of output   (optionally with a title).



Related tasks

   Euler's sum of powers conjecture. 
   Pythagorean triples.


Reference

   the Wikipedia article:   Pythagorean quadruple.


max = 2200;
maxsq = max^2;
d = Range[max]^2;
Dynamic[{a, b, Length[d]}]
Do[
 Do[
  c = Range[1, Floor[(maxsq - a^2 - b^2)^(1/2)]];
  dposs = a^2 + b^2 + c^2;
  d = Complement[d, dposs]
  ,
  {b, Floor[(maxsq - a^2)^(1/2)]}
  ]
 ,
 {a, Floor[maxsq^(1/2)]}
 ]
Sqrt[d]