%I A140411
%S A140411 1,2,5,10,13,37,58,85,130
%N A140411 Conjectured complete list of square-free numbers that can be written 
               as a sum of at most two positive squares, but not as a sum of three 
               positive squares.
%C A140411 Conjecture 1,9, p. 4, of Goswick et al. "The square-free numbers in question 
               form a subset of Euler's numeri idonei [A000926], therefore at most 
               one number can be absent from the list above. If such a number does 
               exist, it must exceed 2 * 10^11 and if it is even the Generalized 
               Riemann Hypothesis is false."
%H A140411 Lee M. Goswick, Emil W. Kiss, Gabor Moussong, Nandor Simanyi, <a href="http:/
               /arxiv.org/pdf/0806.3943">Sums of squares and orthogonal integral 
               vectors</a>
%F A140411 a(n) in A005117 and a(n) in {i^2 + j^2 for i,j > 1} and a(n) not in {i^2 
               + j^2 + k^2 for i,j,k > 1}.
%Y A140411 Cf. A000926, A005117.
%Y A140411 Sequence in context: A018296 A033316 A099194 this_sequence A053353 A099792 
               A115757
%Y A140411 Adjacent sequences: A140408 A140409 A140410 this_sequence A140412 A140413 
               A140414
%K A140411 fini,full,nonn
%O A140411 1,2
%A A140411 Jonathan Vos Post (jvospost3(AT)gmail.com), Jun 25 2008