%I #9 Dec 04 2018 11:02:36
%S 1,2,5,6,10,13,14,21,22,30,37,42,46,58,70,78,93,133,142,190,253
%N Numbers n == 1, 2, 5 or 6 (mod 8) such that there is only one solution to i^2+j^2+k^2=n, i >= j >= k >= 0.
%H P. T. Bateman and E. Grosswald, <a href="https://doi.org/10.1016/0022-314X(84)90074-X">Positive integers expressible as a sum of three squares in essentially only one way</a>, J. Number Theory, 19 (1984), 301-308.
%t aQ[n_] := MemberQ[{1, 2, 5,6}, Mod[n,8]] && Length[Solve[i^2+j^2+k^2==n && k>=0 && j>=k && i>=j, {i,j,k}, Integers]]==1; Select[Range[260], aQ] (* _Amiram Eldar_, Dec 04 2018 *)
%Y Cf. A085616.
%K nonn,fini,full
%O 1,2
%A _N. J. A. Sloane_, Jul 31 2003
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