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arXiv · 1812.04657

Note on sums involving the Euler function

Shane Chern
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Abstract

In this note, we provide refined estimates of the following sums involving the Euler totient function: $$\sum_{n\le x} ϕ\left(\left[\frac{x}{n}\right]\right) \qquad \text{and} \qquad \sum_{n\le x} \frac{ϕ([x/n])}{[x/n]}$$ where $[x]$ denotes the integral part of real $x$. The above summations were recently considered by Bordellès et al. and Wu.

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Shane Chern. 2018-12-11. Note on sums involving the Euler function. https://doi.org/10.1017/s0004972719000066

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