A088017 Numbers not expressible as sum or difference of a nonzero cube and a nonzero square.

6, 14, 16, 21, 27, 29, 32, 34, 42, 46, 51, 58, 59, 62, 66, 69, 70, 75, 77, 78, 84, 85, 86, 88, 90, 93, 96, 102, 103, 110, 111, 114, 115, 123, 125, 130, 133, 137, 140, 144, 149, 157, 158, 160, 162, 165, 166, 173, 176, 178, 179, 181, 182, 183, 187, 194, 201, 202, 203

Offset: 1

Author

Hugo Pfoertner, Sep 18 2003

Keywords

• nonn

Comments

Numbers n such that neither variant of Mordell's equation y^2=x^3+n (A054504) or y^2=x^3-n (A081121) has an integral solution with nonzero x and y. - Jack Brennen, Aug 28 2003

Examples

			16 is in the sequence because the only integral solution to Mordell's equation y^2 = x^3 +- 16 is (y=4,x=0). 49 is not in the sequence because it can also be expressed as 65^3-524^2.
		

Links

• J. Gebel, Integer points on Mordell curves [Cached copy, after the original web site tnt.math.se.tmu.ac.jp was shut down in 2017]
• Eric Weisstein's World of Mathematics, Mordell Curve.

Crossrefs

Cf. A054504, A081121, A087285, A087286.