Is it possible to pick up the value $2<y<x$ to get this expressions simuletansionally $$\sum_{d\leq y}\left \{ \frac{x}{d} \right \}\leqslant \frac{y}{\log^{3} y}?$$ $$\sum_{d\leq y}\left \{ \frac{x+y}{d} \right \}\leqslant \frac{y}{\log^{3} y}?$$
Estimating a sum with a fractional part
user493246
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