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 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 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[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]] (* Jean-François Alcover, Apr 12 2012 *) CROSSREFS Cf. A081120, A081121, A179163-A179175. 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

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Last modified December 9 03:27 EST 2019. Contains 329872 sequences. (Running on oeis4.)