

A094784


Numbers that are neither squares nor cubes.


2



2, 3, 5, 6, 7, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 26, 28, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 82
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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: (1A010052(a(n)))*(1A010057(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)]&] (* JeanFrançois Alcover, Feb 07 2020 *)


PROG

(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)
(PARI) is(n)=!issquare(n) && !ispower(n, 3) \\ Charles R Greathouse IV, Oct 19 2015
(Haskell)
a094784 n = a094784_list !! (n1)
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

A005117 (squarefree numbers) intersect A004709 (cubefree numbers) is A005117; A005117 union A004709 is A004709.
Sequence in context: A071591 A089105 A028769 * A085971 A175082 A007916
Adjacent sequences: A094781 A094782 A094783 * A094785 A094786 A094787


KEYWORD

nonn


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



