A179125 a(n) = A000037(n)^3.

8, 27, 125, 216, 343, 512, 1000, 1331, 1728, 2197, 2744, 3375, 4913, 5832, 6859, 8000, 9261, 10648, 12167, 13824, 17576, 19683, 21952, 24389, 27000, 29791, 32768, 35937, 39304, 42875, 50653, 54872, 59319, 64000, 68921, 74088, 79507, 85184, 91125

Offset

1,1

Comments

Parameters n for which the torsion subgroup of the elliptic curve y^2=x^3+n has order 2.

Numbers which are perfect cubes (A000578) but not perfect squares (A000290).

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Josef Gebel, Integer points on Mordell curves. [Cached copy, after the original web site tnt.math.se.tmu.ac.jp was shut down in 2017]

Josef Gebel, Attila Pethö and Horst G. Zimmer, Computing integral points on Mordell's elliptic curves, Collectanea Mathematica, Vol. 48, No. 1-2 (1997), pp. 115-136; alternative link.

Index to sequences related to elliptic curves

Formula

Sum_{n>=1} 1/a(n) = zeta(3) - zeta(6) = A002117 - A013664 = 0.1847138411... - Amiram Eldar, Nov 21 2020

Mathematica

a[n_]:=(n + Floor[1/2 + Sqrt[n]])^3; Array[a, 50] (* Vincenzo Librandi, Apr 11 2020 *)

Prog

(PARI) isok(n) = !issquare(n) && ispower(n, 3); \\ Michel Marcus, Nov 02 2013
(PARI) a(n) = (n + (1+sqrtint(4*n))\2)^3; \\ Michel Marcus, Nov 02 2013
(Magma) [(n+Floor(1/2+Sqrt(n)))^3: n in [1..60]]; // Vincenzo Librandi, Apr 11 2020

Crossrefs

Cf. A002117, A002151, A002153, A002155, A013664, A102833, A031507.

Sequence in context: A183316 A045971 A176509 * A030160 A030162 A153147

Adjacent sequences: A179122 A179123 A179124 * A179126 A179127 A179128

Keyword

nonn

Author

Artur Jasinski, Jun 30 2010

Extensions

Exponent in the definition corrected by R. J. Mathar, Jul 20 2010

Status

approved