A179145 Numbers n such that Mordell's equation y^2 = x^3 + n has exactly 1 integral solution.

27, 125, 216, 1728, 2197, 3375, 4913, 6859, 8000, 13824, 19683, 24389, 27000, 29791, 59319, 68921, 74088, 79507, 91125, 103823, 110592, 132651, 140608, 148877, 157464, 166375, 195112, 205379, 216000, 226981, 238328, 287496, 300763, 314432

Offset

1,1

Links

Jianing Song, Table of n, a(n) for n = 1..115 (using the b-file of A356720, which is based on the data from A103254)

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]

Formula

a(n) = A356709(n)^3. - Jianing Song, Aug 24 2022

Mathematica

(* Assuming every term is a cube *) xmax = 2000; r[n_] := Reap[ Do[ rpos = Reduce[y^2 == x^3 + n, y, Integers]; If[rpos =!= False, Sow[rpos]]; rneg = Reduce[y^2 == (-x)^3 + n, y, Integers]; If[rneg =!= False, Sow[rneg]], {x, 1, xmax}]]; ok[n_] := Which[ rn = r[n]; rn[[2]] === {}, False, Length[rn[[2]]] > 1, False, ! FreeQ[rn[[2, 1]], Or], False, True, True]; ok[n_ /; !IntegerQ[n^(1/3)]] = False; ok[1]=False; A179145 = Reap[ Do[ If[ok[n], Print[n]; Sow[n]], {n, 1, 320000}]][[2, 1]] (* Jean-François Alcover, Apr 12 2012 *)

Crossrefs

Cf. A054504, A081119, A179145-A179162, A356709.

Complement of A356703 among the positive cubes.

Cf. also A179163, A179419.

Sequence in context: A293894 A137800 A125497 * A369118 A118092 A371189

Adjacent sequences: A179142 A179143 A179144 * A179146 A179147 A179148

Keyword

nonn

Author

Artur Jasinski, Jun 30 2010

Extensions

Edited and extended by Ray Chandler, Jul 11 2010

Status

approved