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%I #28 Sep 08 2022 08:45:13
%S 2,3,5,6,7,10,11,12,13,14,15,17,18,19,20,21,22,23,24,26,28,29,30,31,
%T 32,33,34,35,37,38,39,40,41,42,43,44,45,46,47,48,50,51,52,53,54,55,56,
%U 57,58,59,60,61,62,63,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,82
%N Numbers that are neither squares nor cubes.
%C 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
%C Intersection of A000037 and A007412: (1-A010052(a(n)))*(1-A010057(a(n)))=1. - _Reinhard Zumkeller_, Jul 13 2010
%D R. Honsberger, Mathematical Chestnuts from Around the World, MAA, 2001; see p. 168.
%H Reinhard Zumkeller, <a href="/A094784/b094784.txt">Table of n, a(n) for n = 1..10000</a>
%H J. 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]
%t Select[Range[100], !IntegerQ[#^(1/2)] && !IntegerQ[#^(1/3)]&] (* _Jean-François Alcover_, Feb 07 2020 *)
%o (PARI) g(n) = for(x=0,n,if(!issquare(x)&&!iscube(x),print1(x","))) iscube(n) = { local(r); r = n^(1/3); if(floor(r+.5)^3== n,1,0)
%o (PARI) is(n)=!issquare(n) && !ispower(n,3) \\ _Charles R Greathouse IV_, Oct 19 2015
%o (Haskell)
%o a094784 n = a094784_list !! (n-1)
%o a094784_list = [x | x <- [0..], a010052 x == 0, a010057 x == 0]
%o -- _Reinhard Zumkeller_, Jan 31 2012
%o (Magma) [n: n in [0..90] | not IsSquare(n) and not IsPower(n,3)]; // _Bruno Berselli_, Feb 22 2016
%Y A005117 (squarefree numbers) intersect A004709 (cubefree numbers) is A005117; A005117 union A004709 is A004709.
%K nonn
%O 1,1
%A _Cino Hilliard_, Jun 10 2004
%E Definition corrected by _Rick L. Shepherd_, Aug 11 2004
%E Comment corrected by _Reinhard Zumkeller_, Jul 18 2010
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