Large gaps in the image of the Euler's function

The aim of this note is to provide an upper bound of the number of positive integers $\le x$ which can be written as $φ(n)$ for some positive integer $n$, where $φ$ stands for the Euler's function. The order of magnitude of this estimate, which is roughly $x/\sqrt[4]{\ln x}$, implies that the set of Euler's values contains arbitrarily large gaps.

No reviews yet.

No comments yet.