Problem 416

Erdős Problem #416: declared status 'open'. Formalized: yes. Let $V(x)$ count the number of $n\leq x$ such that $\phi(m)=n$ is solvable. Does $V(2x)/V(x)\to 2$? Is there an asymptotic formula for $V(x)$? Current best: Unfortunately this falls just short of an asymptotic formula for $V(x)$ and determining whether $V(2x)/V(x)\to 2$. In [Er79e] Erd\H{o}s asks further to estimate the number of $n\leq x$ such that the smallest solution to $\phi(m)=n$ satisfies $kx<m\leq (k+1)x$. Prize: no. OEIS: A264810. Tags: number theory.