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%I #7 Sep 24 2022 12:33:31
%S 216,343,1331,12167,13824,17576,21952,29791,54872,74088,85184,103823,
%T 157464,166375,226981,250047,592704,753571,778688,857375,884736,
%U 970299,1124864,1331000,1367631,1404928,1643032,1685159,1906624,2628072
%N Numbers n such that Mordell elliptic curve y^2=x^3-n has a number of integral points that is both odd and > 1.
%C Also positive cubes not in A179163.
%C A000578 = Union({0}, A179163, A179419).
%C Mordell curve y^2=x^3-n always has at least one integral solution if n is a cube, say n=k^3, (x,y)=(k,0). If there are additional solutions, they will exist in pairs - (x,y) and (x,-y). Thus the number of solutions can be odd iff n is a cube.
%Y Cf. A000578, A179163. Cube of A228948.
%K nonn
%O 1,1
%A _Artur Jasinski_, Jul 13 2010
%E Edited and extended by _Ray Chandler_, Jul 14 2010