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A046099 Numbers that are not cubefree. Numbers divisible by a cube greater than 1. Complement of A004709. 34
8, 16, 24, 27, 32, 40, 48, 54, 56, 64, 72, 80, 81, 88, 96, 104, 108, 112, 120, 125, 128, 135, 136, 144, 152, 160, 162, 168, 176, 184, 189, 192, 200, 208, 216, 224, 232, 240, 243, 248, 250, 256, 264, 270, 272, 280, 288, 296, 297, 304, 312, 320, 324, 328, 336 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Also called cubeful numbers, but this term is ambiguous and is best avoided.

Numbers n such that A007427(n) = sum(d|n,mu(d)*mu(n/d)) == 0. - Benoit Cloitre, Apr 17 2002

The convention in the OEIS is that squareful, cubeful, biquadrateful (A046101), ... mean the same as "not squarefree" etc., while 2- or square-full, 3- or cube-full (A036966), 4-full (A036967) are used for Golomb's notion of powerful numbers (A001694, see references there), when each prime factor occurs to a power > 1. - M. F. Hasler, Feb 12 2008

Also solutions to equation tau_{-2}(n)=0, where tau_{-2} is A007427. - Enrique Pérez Herrero, Jan 19 2013

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

LINKS

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

Eric Weisstein's World of Mathematics, Cubefree.

FORMULA

A212793(a(n)) = 0. - Reinhard Zumkeller, May 27 2012

MAPLE

isA046099 := proc(n)

    local p;

    for p in ifactors(n)[2] do

        if op(2, p) >= 3 then

            return true;

        end if;

    end do:

    false ;

end proc:

for n from 1 do

    if isA046099(n) then

        printf("%d\n", n) ;

    end if;

end do: # R. J. Mathar, Dec 08 2015

MATHEMATICA

lst={}; Do[a=0; Do[If[FactorInteger[m][[n, 2]]>2, a=1], {n, Length[FactorInteger[m]]}]; If[a==1, AppendTo[lst, m]], {m, 10^3}]; lst (* Vladimir Joseph Stephan Orlovsky, Aug 15 2008 *)

PROG

(Haskell)

a046099 n = a046099_list !! (n-1)

a046099_list = filter ((== 1) . a212793) [1..]

-- Reinhard Zumkeller, May 27 2012

(PARI) is(n)=n>7 && vecmax(factor(n)[, 2])>2 \\ Charles R Greathouse IV, Sep 17 2015

CROSSREFS

Complement of A004709.

Subsequences: A000578 and A030078.

Cf. A036966, A046101, A001694.

Sequence in context: A048108 A228957 A137845 * A033859 A177899 A246311

Adjacent sequences:  A046096 A046097 A046098 * A046100 A046101 A046102

KEYWORD

nonn

AUTHOR

Eric W. Weisstein

EXTENSIONS

More terms from Vladimir Joseph Stephan Orlovsky, Aug 15 2008

Edited by N. J. A. Sloane, Jul 27 2009

STATUS

approved

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Last modified July 24 16:44 EDT 2017. Contains 289775 sequences.