OPENHARDnumber theory
Schoenberg proved that for every $c\in [0,1]$ the density of $\{ n\in \mathbb{N} : \phi(n)<cn\}$ exists. Let this density be denoted by $f(c)$. Is it true that there are no $x$ such that $f'(x)$ exists and is positive?
Notes: Erdos could prove the distribution function is purely singular.
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