Erdős Problem 51

Reference: erdosproblems.com/51

theorem Erdos51.erdos_51 : (∃ (A : Set ℕ) (n : ↑A → ℕ), A.Infinite ∧ (∀ (a : ↑A), IsLeast (Nat.totient ⁻¹' {↑a}) (n a)) ∧ Filter.Tendsto (fun (a : ↑A) => ↑(n a) / ↑↑a) Filter.atTop Filter.atTop) ↔ sorry

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 $\frac{n_a}{a} → \infty$ as $a → ∞$?