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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 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 May 20 03:10 EDT 2019. Contains 323412 sequences. (Running on oeis4.)