By Shane Chern

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

December 11, 2018

Loading full text...

Similar articles

Loading recommendations...

x1

Note on sums involving the Euler function

Click on play to start listening