%I #3 Mar 30 2012 17:22:33
%S 14,21,26,29,30,35,38,41,42,45,46,49,50,53,54,59,61,65,66,70,75,78,81,
%T 83,91,93,106,107,109,113,114,115,118,121,133,137,139,142,145,147,153,
%U 157,162,169,171,178,190,198,202,205,211,214,219,226,235,243,253,258,262,265,277,283,289,291,298,307,313,323,331,337,358,363,379,387,397,403,418,427,438,442,445,457,466,498,499,505,547,562,577,603,643,723,793,883,907,1003,1227,1243,1387,1411,1467,1507
%N Numbers n such that 4^k*n, for k >= 0, have a unique partition into three distinct positive squares.
%C It is conjectured that this sequence is complete.
%e 793 is in this sequence because 793 = 6^2 + 9^2 + 26^2 is the unique partition of 793.
%t lim=100; 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]}]; Select[Flatten[Position[nLst, 1]], Mod[ #, 4]>0&]
%Y Cf. A094739 (primitive n having a unique partition into three squares), A094740 (primitive n having a unique partition into three positive squares).
%K nonn,fini,full
%O 1,1
%A _T. D. Noe_, Jun 15 2004