

A046099


Numbers that are not cubefree. Numbers divisible by a cube greater than 1. Complement of A004709.


41



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
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OFFSET

1,1


COMMENTS

Also called cubeful numbers, but this term is ambiguous and is best avoided.
Numbers n such that A007427(n) = sum(dn,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 squarefull, 3 or cubefull (A036966), 4full (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 biunitary 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 !! (n1)
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



