Abstract
Let φ be the Euler's function. A question of Rosser and Schoenfeld is answered, showing that there exists infinitely many n such that n φ(n) > e y log log n , where γ is the Euler's constant. More precisely, if N k is the product of the first k primes, it is proved that, under the Riemann's hypothesis, N k φ(N k) > e y log log N k holds for any k ≥ 2, and, if the Riemann's hypothesis is false this inequality holds for infinitely many k, and is false for infinitely many k.
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