On a sum involving the Euler function

We obtain reasonably tight upper and lower bounds on the sum $\sum_{n \leqslant x} \varphi \left( \left\lfloor{x/n}\right\rfloor\right)$, involving the Euler functions $\phi$ and the integer parts $\lfloor x\mathrm{/}n\rfloor$ of the reciprocals of integers.