Abstract
In this short note, we prove that 4π2xlogx+O(x)⩽∑n⩽xφ([xn])⩽(13+4π2)xlogx+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 of Bordellès–Heyman–Shparlinski and of Dai–Pan.
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