A080762 Positive numbers not of the form y^2 - x^3, x and y >= 1.

2, 4, 5, 6, 7, 10, 11, 13, 14, 16, 20, 21, 23, 25, 26, 27, 29, 31, 32, 33, 34, 39, 42, 43, 45, 46, 47, 49, 50, 51, 52, 53, 58, 59, 60, 61, 62, 66, 67, 69, 70, 72, 74, 75, 76, 77, 78, 81, 82, 83, 84, 85, 86, 87, 88, 90, 91, 93, 95, 96, 102, 103, 104, 109, 110, 111, 114, 115

Offset: 1

Author

Cino Hilliard, Mar 10 2003

Keywords

• nonn

Comments

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

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]J. Gebel, Integer points on Mordell curves
• J. Gebel, A. Petho and H. G. Zimmer, On Mordell's equation, Compositio Math. 110 (1998), 335-367.

Crossrefs

Complement of A080761.

Programs

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" ")) ) }