Abstract
Let Φ(x) denote the number of those integers n with ϕ(n)≤ x, where ϕ denotes the Euler function. Improving on a well-known estimate of Bateman (1972), we show that Φ(x)-Ax ≪ R(x), where A=ζ(2)ζ(3)/ζ(6) and R(x) is essentially of the size of the best available estimate for the remainder term in the prime number theorem.
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Balazard, M., Tenenbaum, G. Sur la répartition des valeurs de la fonction d'Euler. Compositio Mathematica 110, 239–250 (1998). https://doi.org/10.1023/A:1000285612395
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DOI: https://doi.org/10.1023/A:1000285612395