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This paper is concerned with the function $r_{k,s}(n)$, the number of(ordered) representations of $n$ as the sum of $s$ positive $k$-th powers,where integers $k,s\ge 2$. We examine the mean average of the function, orequivalently, \begin{equation*} \sum_{m=1}^n r_{k,s}(m). \end{equation*}

On the mean average of integer partition as the sum of powers