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A179145 Numbers n such that Mordell's equation y^2 = x^3 + n has exactly 1 integral solution. 18
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..34.

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]

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.

Sequence in context: A293894 A137800 A125497 * A118092 A126272 A016755

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

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Last modified April 18 02:38 EDT 2021. Contains 343072 sequences. (Running on oeis4.)