Quasiperfect numbers with the same exponent

We study some divisibility properties of quasiperfect numbers. We show that if $N=(p_1{p}_2\cdots p_t{)}^{2a}=m^2$ is quasiperfect, then $2a+1$ is divisible by $3$ and $N$ has at least one prime factor smaller than $\exp 716.7944$. Moreover, we find some lower bounds concerning quasiperfect numbers of the form $N=m^2$ with $m$ squarefree.