  Denote by $N(n)$ the number of integer solutions $(x_1,\,x_2,\ldots ,x_n)$ of
the equation $x_1+x_2+\ldots+x_n=x_1x_2\cdot\ldots\cdot x_n$ such that $x_1\ge
x_2\ge\ldots\ge x_n\ge 1$, $n \in \mathbb{Z}^+$. The aim of this paper are is
twofold: first we present an asymptotic formula for $\sum\limits_{2\le n\le
x}N(n)$, then we verify that the counting function $N(n)$ takes very large
value compared to its average value.
