The asymptotic number of
[square-free numbers](http://en.wikipedia.org/wiki/Square-free_integer#Distribution)
$\le n$ is $Q(n) = 6n/\pi^2 + O(\sqrt{n})$.
Because
[$\zeta(2)=\pi^2/6$](http://mathworld.wolfram.com/RiemannZetaFunctionZeta2.html),
$Q(n) \approx n/\zeta(2)$.

[OEIS A004709](http://oeis.org/A004709)
says that cube-free numbers have asymptotic density of
$1/\zeta(3)$, "the reciprocal of
[Apery's constant](http://mathworld.wolfram.com/AperysConstant.html)"
("the probability that three randomly chosen integers are relatively prime":
[link here](http://oeis.org/A088453)).

> ***Q***. Are there analogous results or conjectures for $k^{\textrm{th}}$-power-free numbers?, $k>3$?
Does the density continue to $1/\zeta(k)$? Is that conjectured or proven or disproven?

I ask this in (obvious) number-theoretic naiveté.
<hr />
**Answered** by Gjergji Zaimi and Douglas Zare: the density indeed grows
as $1/\zeta(k)$, and this has been established.