Erdős Problem #417

Let\[V'(x)=\#\{\phi(m) : 1\leq m\leq x\}\]and\[V(x)=\#\{\phi(m) \leq x : 1\leq m\}.\]Does $\lim V(x)/V'(x)$ exist? Is it $>1$?

#417: [Er79e][ErGr80][Er98]

number theory

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It is trivial that $V'(x) \leq V(x)$. In [Er98] Erdős suggests the limit may be infinite. See also [416].

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Related OEIS sequences: A264810 A061070

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