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Search: id:A004709
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| A004709 |
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Cube-free numbers: numbers that are not divisible by any cube > 1. |
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33
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| 1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 25, 26, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 55, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 82, 83, 84, 85
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Numbers n such that no smaller number m satisfies kronecker(n,k)=kronecker(m,k) for all k. - Michael Somos Sep 22 2005
Contribution from Gerard P. Michon (g.michon(AT)att.net), May 06 2009: (Start)
The asymptotic density of cubefree integers is the reciprocal of Apery's constant
1 / zeta(3) = 0.831907372580707468683126278821530734417... (cf. A088453) (End)
A066990(a(n)) = a(n). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jun 25 2009]
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
G. P. Michon, On the number of cubefree integers not exceeding N. [From Gerard P. Michon (g.michon(AT)att.net), May 06 2009]
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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MATHEMATICA
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lst={}; Do[a=0; Do[If[FactorInteger[m][[n, 2]]>2, a=1], {n, Length[FactorInteger[m]]}]; If[a!=1, AppendTo[lst, m]], {m, 6!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Sep 27 2008]
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PROGRAM
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(PARI) {a(n)= local(m, c); if(n<2, n==1, c=1; m=1; while( c<n, m++; if( 3>vecmax(factor(m)[, 2]), c++)); m)} /* Michael Somos Sep 22 2005 */
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CROSSREFS
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Complement of A046099.
Cf. A005117 = square-free numbers, A067259 = cube-free numbers which are not square-free, A046099 = cubeful numbers.
Cf. A160112, A160113, A160114 & A160115: On the number of cubefree integers. [From Gerard P. Michon (g.michon(AT)att.net), May 06 2009]
Sequence in context: A043093 A023802 A007915 this_sequence A048107 A078129 A003796
Adjacent sequences: A004706 A004707 A004708 this_sequence A004710 A004711 A004712
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KEYWORD
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nonn,easy
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AUTHOR
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Steven.Finch(AT)inria.fr (S. R. Finch)
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