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A179419 Numbers n such that Mordell elliptic curve y^2=x^3-n has a number of integral points that is both odd and > 1. 4
216, 343, 1331, 12167, 13824, 17576, 21952, 29791, 54872, 74088, 85184, 103823, 157464, 166375, 226981, 250047, 592704, 753571, 778688, 857375, 884736, 970299, 1124864, 1331000, 1367631, 1404928, 1643032, 1685159, 1906624, 2628072 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Also positive cubes not in A179163.
A000578 = Union({0}, A179163, A179419).
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.
LINKS
CROSSREFS
Cf. A000578, A179163. Cube of A228948.
Sequence in context: A204650 A115430 A278976 * A224549 A339245 A327284
KEYWORD
nonn
AUTHOR
Artur Jasinski, Jul 13 2010
EXTENSIONS
Edited and extended by Ray Chandler, Jul 14 2010
STATUS
approved

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Last modified June 25 04:03 EDT 2024. Contains 373697 sequences. (Running on oeis4.)