A positive integer $N$ is said to be $k$-multiperfect if
$$\sigma(N) = kN$$
where $\sigma(x)$ is the sum of the divisors of $x$ and $k$ is a positive integer.
(The case $k = 2$ reduces to the original notion of perfect numbers.)
Now my question is the following: Are all known $k$-multiperfect numbers (for $k > 2$) not squarefree?
For the case $k = 2$, the only known exception is $N = 6 = 2\cdot3$.
Update [October 06 2013 - Manila time] :: This question has been cross-posted to MathOverflow here.