%I #7 Aug 16 2016 12:02:26
%S 7,10,14,15,18,22,23,25,26,27,28,30,31,35,38,39,40,42,43,46,47,49,50,
%T 51,54,55,56,57,58,60,62,63,65,66,67,70,71,72,73,74,75,78,79,81,82,83,
%U 86,87,88,90,91,92,94,95,97,98,99,100,102,103,104,105,106
%N Integral averages of three distinct squares.
%C 7 = (1^2 + 2^2 + 4^2)/3
%C 10 = (1^2 + 2^2 + 5^2)/3
%C 14 = (1^2 + 4^2 + 5^2)/3
%C First case with 2 ways: 23 = (1^2 + 2^2 + 8^2)/3 = (2^2 + 4^2 + 7^2)/3
%C 42 has 3 sets of triples {a,b,c} such that 42= (a^2 + b^2 + c^2)/3: {1,2,11}, {1,5,10}, {3,6,9}
%C 63 has 4 sets of triples {a,b,c}: {2,4,13}, {2,8,11}, {3,6,12}, {5,8,10}, etc.
%H Zak Seidov, <a href="/A215579/b215579.txt">Table of n, a(n) for n = 1..1000</a>
%t Take[Select[Mean/@Subsets[Range[20]^2,{3}],IntegerQ]//Union,70] (* _Harvey P. Dale_, Aug 16 2016 *)
%K nonn
%O 1,1
%A _Zak Seidov_, Aug 16 2012
