login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A004709 Cubefree numbers: numbers that are not divisible by any cube > 1. 63
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; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Also called cube-free numbers. - N. J. A. Sloane, Oct 18 2015

Numbers n such that no smaller number m satisfies: kronecker(n,k)=kronecker(m,k) for all k. - Michael Somos, Sep 22 2005

The asymptotic density of cubefree integers is the reciprocal of Apery's constant 1/zeta(3) = A088453. - Gerard P. Michon, May 06 2009

A066990(a(n)) = a(n). - Reinhard Zumkeller, Jun 25 2009

A212793(a(n)) = 1. - Reinhard Zumkeller, May 27 2012

Numbers whose sum of bi-unitary divisors is equal to the sum of unitary divisors: A188999(n) = A034448(n). - Paolo P. Lava, Sep 25 2014

A124010(a(n),k) <= 2 for all k = 1..A01221(a(n)). - Reinhard Zumkeller, Mar 04 2015

LINKS

T. D. Noe, Table of n, a(n) for n=1..1000

G. P. Michon, On the number of cubefree integers not exceeding N.

V. Shevelev, Set of all densities of exponentially S-numbers, arXiv preprint arXiv:1511.03860 [math.NT], 2015.

Eric Weisstein's World of Mathematics, Cubefree

MAPLE

isA004709 := proc(n)

    local p;

    for p in ifactors(n)[2] do

        if op(2, p) > 2 then

            return false;

        end if;

    end do:

    true ;

end proc:

MATHEMATICA

Select[Range[6!], FreeQ[FactorInteger[#], {_, k_ /; k > 2}] &] (* Jan Mangaldan, May 07 2014 *)

PROG

(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 */

(Haskell)

a004709 n = a004709_list !! (n-1)

a004709_list = filter ((== 1) . a212793) [1..]

-- Reinhard Zumkeller, May 27 2012

CROSSREFS

Complement of A046099.

Cf. A005117 (squarefree), A067259 (cubefree but not squarefree), A046099 (cubeful).

Cf. A160112, A160113, A160114 & A160115: On the number of cubefree integers. - Gerard P. Michon, May 06 2009

Cf. A030078.

Cf. A001221, A124010, A212793.

Sequence in context: A043093 A023802 A007915 * A048107 A078129 A188437

Adjacent sequences:  A004706 A004707 A004708 * A004710 A004711 A004712

KEYWORD

nonn,easy

AUTHOR

Steven Finch, Jun 14 1998

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified March 25 01:30 EDT 2017. Contains 284036 sequences.