Note on a sum involving the Euler function

2018/09/27 by Dai, Li-Xia, Pan, Hao
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1809.10381

Abstract

We prove that ∑_{n ≤ x} φ([x/n])≤((1380)/(4009)+(2629)/(4009)⋅\frac1ζ(2)+o(1))xlog x as x→∞, where φ denotes the Euler totient function and [x] denotes the integer part of x.

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