

A179163


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


13



1, 8, 27, 64, 125, 512, 729, 1000, 1728, 2197, 2744, 3375, 4096, 4913, 5832, 6859, 8000, 9261, 10648, 15625, 19683, 24389, 27000, 32768, 35937, 39304, 42875, 46656, 50653, 59319, 64000, 68921, 79507, 91125, 97336, 110592, 117649, 125000, 132651
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OFFSET

1,2


LINKS

Table of n, a(n) for n=1..39.
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[1] = True; 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; A179163 = Reap[Do[If[ok[n], Print[n]; Sow[n]], {n, 1, 140000}]][[2, 1]] (* JeanFrançois Alcover, Apr 12 2012 *)


CROSSREFS

Cf. A081120, A081121, A179163A179175.
Sequence in context: A111131 A111103 A076969 * A050462 A112662 A121652
Adjacent sequences: A179160 A179161 A179162 * A179164 A179165 A179166


KEYWORD

nonn


AUTHOR

Artur Jasinski, Jun 30 2010


EXTENSIONS

Edited and extended by Ray Chandler, Jul 11 2010


STATUS

approved



