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%I #3 Mar 30 2012 17:22:33
%S 3,6,9,11,14,17,18,19,21,22,26,29,30,34,35,42,43,45,46,49,50,53,61,65,
%T 67,70,73,78,82,91,93,97,106,109,115,133,142,145,157,163,169,190,193,
%U 202,205,235,253,265,277,298,397,403,427,442,445,505,793
%N Numbers n such that 4^k n, for k >= 0, are numbers having a unique partition into three 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, Sqrt[lim^2-a^2]}, {c, b, Sqrt[lim^2-a^2-b^2]}]; Select[Flatten[Position[nLst, 1]], Mod[ #, 4]>0&]
%Y Cf. A094739 (n having a unique partition into three squares).
%K nonn
%O 1,1
%A _T. D. Noe_, May 24 2004
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