The Error Term of the Summatory Euler Phi Function

A sharper estimate for the summatory Euler phi function $\sum_{n \leq x} \varphi(n)$ is presented in this work. It improves the established estimate in the current mathematical literature. In addition, an estimate for its reciprocal ${\sum }_{n\le x}1\mathrm{/}\phi (n)$ is also determined.