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A179145 Numbers n such that Mordell's equation y^2 = x^3 + n has exactly 1 integral solution. 24
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
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
Complement of A356703 among the positive cubes.
Cf. also A179163, A179419.
Sequence in context: A293894 A137800 A125497 * A369118 A118092 A371189
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 June 16 07:19 EDT 2024. Contains 373423 sequences. (Running on oeis4.)