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NOTE ON SUMS INVOLVING THE EULER FUNCTION
Published online by Cambridge University Press: 07 February 2019
Abstract
In this note, we provide refined estimates of two sums involving the Euler totient function, $$\begin{eqnarray}\mathop{\sum }_{n\leq x}\unicode[STIX]{x1D719}\biggl(\biggl[\frac{x}{n}\biggr]\biggr)\quad \text{and}\quad \mathop{\sum }_{n\leq x}\frac{\unicode[STIX]{x1D719}([x/n])}{[x/n]},\end{eqnarray}$$
$[x]$ denotes the integral part of real
$x$. The above summations were recently considered by Bordellès et al. [‘On a sum involving the Euler function’, Preprint, 2018, arXiv:1808.00188] and Wu [‘On a sum involving the Euler totient function’, Preprint, 2018, hal-01884018].
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- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 100 , Issue 2 , October 2019 , pp. 194 - 200
- Copyright
- © 2019 Australian Mathematical Publishing Association Inc.