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A094784 Numbers that are neither squares nor cubes. 1
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 (list; graph; refs; listen; history; text; internal format)
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. [From Artur Jasinski, Jun 30 2010]

Intersection of A000037 and A007412: (1-A010052(a(n)))*(1-A010057(a(n)))=1. [From 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

Gebel J., Integer points on Mordell curves [From Artur Jasinski, Jun 30 2010]

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)

(Haskell)

a094784 n = a094784_list !! (n-1)

a094784_list = [x | x <- [0..], a010052 x == 0, a010057 x == 0]

-- Reinhard Zumkeller, Jan 31 2012

CROSSREFS

A005117 (squarefree numbers) intersect A004709 (cube-free numbers) would be A005117; A005117 union A004709 would be 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

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Last modified August 31 04:27 EDT 2014. Contains 246235 sequences.