Problem 51

Erdős Problem #51: declared status 'open'. Formalized: yes. Is there an infinite set $A\subset \mathbb{N}$ such that for every $a\in A$ there is an integer $n$ such that $\phi(n)=a$, and yet if $n_a$ is the smallest such integer then $n_a/a\to \infty$ as $a\to\infty$? Prize: no. OEIS: A002202, A014197. Tags: number theory.