Li-Xia Dai

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20112018

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math.NT2018

Note on a sum involving the Euler function

Li-Xia Dai, Hao Pan

We prove that $n \leq x \sum φ ([x / n]) \leq (\frac{1380}{4009} + \frac{2629}{4009} \cdot \frac{1}{ζ ( 2 )} + o (1)) x lo g x$ as $x \to \infty$ , where $φ$ denotes the Euler totient fu…

math.NT2018

On a sum involving the Euler function

Olivier Bordellès, Lixia Dai, Randell Heyman +2

We obtain reasonably tight upper and lower bounds on the sum $\sum_{n ⩽ x} φ (⌊ x / n ⌋)$ , involving the Euler functions $φ$ and the integer…