A356703 Numbers k such that Mordell elliptic curve y^2 = x^3 + k has a number of integral points that is both odd and > 1.

1, 8, 64, 343, 512, 729, 1000, 1331, 2744, 4096, 5832, 9261, 10648, 12167, 15625, 17576, 21952, 32768, 35937, 39304, 42875, 46656, 50653, 54872, 64000, 85184, 97336, 117649, 125000, 175616, 185193, 250047, 262144, 274625, 343000, 357911, 373248, 405224, 474552, 531441, 592704, 636056

Offset

1,2

Comments

Cubes k such that y^2 = x^3 + k has a solution other than (-k^(1/3), 0).

Contains all sixth powers since A179149 does.

Links

Jianing Song, Table of n, a(n) for n = 1..85

Formula

a(n) = A356720(n)^3.

Example

512 is a term since the equation y^2 = x^3 + 512 has 9 integral solutions (-8,0), (-7,+-13), (4,+-24), (8,+-32), and (184,+-2496).

Crossrefs

Complement of A179145 among the positive cubes.

Cf. A081119, A179147, A179149, A179151, A179163, A179419.

Cf. also A356709, A356720, A356713, A228948.

Sequence in context: A188875 A344854 A223843 * A267189 A181480 A223948

Adjacent sequences: A356700 A356701 A356702 * A356704 A356705 A356706

Keyword

nonn

Author

Jianing Song, Aug 23 2022

Status

approved