  In this paper, we can show that \begin{align*} S_{\Lambda}(x)=\sum_{1\leq
n\leq x}\Lambda \left(\left[\frac{x}{n}\right]\right)= \sum_{n=1}^{\infty}
\frac{\Lambda(n)}{n(n+1)}x +O\left(x^{7/15+1/195+\varepsilon}\right),
\end{align*} where $\Lambda(n)$ is the von Mangdolt function. Moreover, we can
also give a similar result related to the divisor function, which improves
previous results.

Number Theory