On a sum involving the Euler totient function

J. Wu (1)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

In this short note, we prove that 4 π 2 x log x + O(x) nx ϕ x n 1 3 + 4 π 2 x log x + O(x), for x → ∞, where ϕ(n) is the Euler totient function and [t] is the integral part of real t. This improves recent results ofBordelì es-Heyman-Shparlinski and of Dai-Pan.

Domaines: Théorie des nombres [math.NT]

J. Wu. On a sum involving the Euler totient function. 2018. ⟨hal-01884018v1⟩