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Problem on Euler's Phi function
Let $S(n)$ be $S(n)=\left\{k\;\left|\;\left\{\frac{n}{k}\right\}\right.\geq \frac{1}{2}\right\}$,where $\{x\}$ is the fractional part of $x$
Prove that :
\begin{align}
\sum_{k\in S(n)} ...