I asked the following question in MSE four ($4$) days ago, but so far nobody has posted an answer.
The gist of the question is as follows:
Are all known $k$-multiperfect numbers (for $k > 2$) not squarefree?
From my own computational verifications using WolframAlpha, it appears that a closely related question is:
Are all known (even) $k$-multiperfect numbers (for $k > 2$) divisible by $4$?