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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 $>1$?
It is trivial that $V'(x) \leq V(x)$. See also [416].