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%I #3 Mar 30 2012 17:22:33
%S 1507,4323,5947,10707,19723,30067,34483,47107,58843,77683,111763,
%T 106723,126043,166147,164803,222643,217627,232243,289963,319243,
%U 300787,319867,462883,393187,546067,532123,502483,615883,662803,606643
%N Greatest number, not divisible by 4, having exactly n partitions into three distinct positive squares.
%C These are conjectured values. The Mathematica program checks numbers up to 10^6.
%t lim=1000; nLst=Table[0, {lim^2}]; Do[n=a^2+b^2+c^2; If[n>0 && n<lim^2, nLst[[n]]++ ], {a, lim}, {b, a+1, Sqrt[lim^2-a^2]}, {c, b+1, Sqrt[lim^2-a^2-b^2]}]; Table[Last[Select[Flatten[Position[nLst, k]], Mod[ #, 4]>0&]], {k, 30}]
%Y Cf. A025415 (least sum of 3 distinct nonzero squares in exactly n ways).
%K nonn
%O 1,1
%A _T. D. Noe_, Jun 15 2004