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%I #30 Sep 08 2022 08:45:54
%S 8,27,125,216,343,512,1000,1331,1728,2197,2744,3375,4913,5832,6859,
%T 8000,9261,10648,12167,13824,17576,19683,21952,24389,27000,29791,
%U 32768,35937,39304,42875,50653,54872,59319,64000,68921,74088,79507,85184,91125
%N a(n) = A000037(n)^3.
%C Parameters n for which the torsion subgroup of the elliptic curve y^2=x^3+n has order 2.
%C Numbers which are perfect cubes (A000578) but not perfect squares (A000290).
%H Amiram Eldar, <a href="/A179125/b179125.txt">Table of n, a(n) for n = 1..10000</a>
%H Josef Gebel, <a href="/A001014/a001014.txt">Integer points on Mordell curves</a>. [Cached copy, after the original web site tnt.math.se.tmu.ac.jp was shut down in 2017]
%H Josef Gebel, Attila Pethö and Horst G. Zimmer, <a href="https://www.raco.cat/index.php/CollectaneaMathematica/article/view/56380">Computing integral points on Mordell's elliptic curves</a>, Collectanea Mathematica, Vol. 48, No. 1-2 (1997), pp. 115-136; <a href="https://eudml.org/doc/40418">alternative link</a>.
%H <a href="/index/El#elliptic">Index to sequences related to elliptic curves</a>
%F Sum_{n>=1} 1/a(n) = zeta(3) - zeta(6) = A002117 - A013664 = 0.1847138411... - _Amiram Eldar_, Nov 21 2020
%t a[n_]:=(n + Floor[1/2 + Sqrt[n]])^3; Array[a,50] (* _Vincenzo Librandi_, Apr 11 2020 *)
%o (PARI) isok(n) = !issquare(n) && ispower(n, 3); \\ _Michel Marcus_, Nov 02 2013
%o (PARI) a(n) = (n + (1+sqrtint(4*n))\2)^3; \\ _Michel Marcus_, Nov 02 2013
%o (Magma) [(n+Floor(1/2+Sqrt(n)))^3: n in [1..60]]; // _Vincenzo Librandi_, Apr 11 2020
%Y Cf. A002117, A002151, A002153, A002155, A013664, A102833, A031507.
%K nonn
%O 1,1
%A _Artur Jasinski_, Jun 30 2010
%E Exponent in the definition corrected by _R. J. Mathar_, Jul 20 2010
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