%I #20 Mar 13 2023 10:21:08
%S 2,4,5,6,7,10,11,13,14,16,20,21,23,25,26,27,29,31,32,33,34,39,42,43,
%T 45,46,47,49,50,51,52,53,58,59,60,61,62,66,67,69,70,72,74,75,76,77,78,
%U 81,82,83,84,85,86,87,88,90,91,93,95,96,102,103,104,109,110,111,114,115
%N Positive numbers not of the form y^2 - x^3, x and y >= 1.
%C This is Mordell's equation with the condition that x and y are positive. Sequence A054504 lists the n for which there is no solution to Mordell's equation (positive or negative x and y). Hence, all of those numbers will be in this sequence. Additional terms of this sequence can be determined by looking at the link to Gebel's data. - _T. D. Noe_, Mar 23 2011
%H J. Gebel, <a href="/A001014/a001014.txt">Integer points on Mordell curves</a> [Cached copy, after the original web site tnt.math.se.tmu.ac.jp was shut down in 2017]J. Gebel, <a href="http://tnt.math.se.tmu.ac.jp/simath/MORDELL/">Integer points on Mordell curves</a>
%H J. Gebel, A. Petho and H. G. Zimmer, <a href="http://dx.doi.org/10.1023/A:1000281602647">On Mordell's equation</a>, Compositio Math. 110 (1998), 335-367.
%o (PARI) diop(n,m) = {f=0; for(p=1,m, f=0; for(x=1,n, y=x*x*x+p; if(issquare(y),f=1); ); if(f==0,print1(p" ")) ) }
%Y Complement of A080761.
%K nonn
%O 1,1
%A _Cino Hilliard_, Mar 10 2003