Abstract:
Suppose that $k$ and $l$ are integers such that $k\ge2$ and $l\ge2$ , $M_k$ is a set of numbers without $k$th powers, and $\tau(n)=\sum_{d\mid n}1$. In this paper, we obtain asymptotic estimates of the sums $\sum\tau(n)\tau(n+1)$ over $n\le x$, $n\in M_k$.
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