  Let $\ba=(a_1,a_2,\ldots,a_k)$, where $a_j \ (j=1,\ldots,k)$ are positive
integers such that $a_1 \leq a_2 \leq \cdots \leq a_k$. Let
$d(\ba;n)=\sum_{n_1^{a_1}\cdots n_k^{a_k}=n}1$ and $\Delta(\ba;x)$ be the error
term of the summatory function of $d(\ba;n)$. In this paper we show an
asymptotic formula of the mean square of $\Delta(\ba;x)$ under a certain
condition. Furthermore, in the cases $k=2$ and 3, we give unconditional
asymptotic formulas for these mean squares.
