On a sum involving the Euler function

By O. Bordellès, Li-Xia Dai, Randell Heyman, Hao Pan, Igor E. Shparlinski. Journal of Number Theory, 2018

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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 $\varphi$ and the integer parts $\left\lfloor{x/n}\right\rfloor$ of the reciprocals of integers.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics

View Paper: https://www.semanticscholar.org/paper/3203131306adb35ee4bf9c4ba01c34e51cf7f229