1,1

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]

a(n) = A356709(n)^3. - Jianing Song, Aug 24 2022

(* 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 *)

Cf. A054504, A081119, A179145-A179162, A356709.

Complement of A356703 among the positive cubes.

Cf. also A179163, A179419.

Sequence in context: A293894 A137800 A125497 * A381825 A369118 A118092

Adjacent sequences: A179142 A179143 A179144 * A179146 A179147 A179148

Artur Jasinski, Jun 30 2010

Edited and extended by Ray Chandler, Jul 11 2010

approved