  We prove that $$ \sum_{n \leq x}
\varphi([x/n])\leq\bigg(\frac{1380}{4009}+\frac{2629}{4009}\cdot\frac1{\zeta(2)}+o(1)\bigg)x\log
x $$ as $x\to\infty$, where $\varphi$ denotes the Euler totient function and
$[x]$ denotes the integer part of $x$.
