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

Author

Artur Jasinski, Jun 30 2010

Keywords

• nonn

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

Crossrefs

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

Programs

Magma

[(n+Floor(1/2+Sqrt(n)))^3: n in [1..60]]; // Vincenzo Librandi, Apr 11 2020

Mathematica

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

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

Python

from math import isqrt
def A179125(n): return (n+(k:=isqrt(n))+int(n>k*(k+1)))**3 # Chai Wah Wu, Jun 05 2025

Formula

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

Extensions

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