

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.


 
 
   Filter =: (#~`)(`:6)
 
   B =: *: A =: i. >: i. 2200
 
   S1 =: , B +/ B             NB. S1 is a raveled table of the sums of squares
   S1 =: <:&({:B)Filter S1    NB. remove sums of squares exceeding bound
   S1 =: ~. S1                NB. remove duplicate entries
 
   S2 =: , B +/ S1
   S2 =: <:&({:B)Filter S2
   S2 =: ~. S2
 
   RESULT =: (B -.@:e. S2) # A
   RESULT
1 2 4 5 8 10 16 20 32 40 64 80 128 160 256 320 512 640 1024 1280 2048
 
 