OFFSET
1,1
COMMENTS
Numbers n for which order of torsion subgroup t of the elliptic curve y^2=x^3+n is t=1. - Artur Jasinski, Jun 30 2010
Intersection of A000037 and A007412: (1-A010052(a(n)))*(1-A010057(a(n)))=1. - Reinhard Zumkeller, Jul 13 2010
REFERENCES
R. Honsberger, Mathematical Chestnuts from Around the World, MAA, 2001; see p. 168.
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
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]
MATHEMATICA
Select[Range[100], !IntegerQ[#^(1/2)] && !IntegerQ[#^(1/3)]&] (* Jean-François Alcover, Feb 07 2020 *)
PROG
(PARI) is(n)=!issquare(n) && !ispower(n, 3) \\ Charles R Greathouse IV, Oct 19 2015
(Haskell)
a094784 n = a094784_list !! (n-1)
a094784_list = [x | x <- [0..], a010052 x == 0, a010057 x == 0]
-- Reinhard Zumkeller, Jan 31 2012
(Magma) [n: n in [0..90] | not IsSquare(n) and not IsPower(n, 3)]; // Bruno Berselli, Feb 22 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Cino Hilliard, Jun 10 2004
EXTENSIONS
Definition corrected by Rick L. Shepherd, Aug 11 2004
Comment corrected by Reinhard Zumkeller, Jul 18 2010
STATUS
approved