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 $a → ∞$?

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1True ↔2  ∃ A n,3    A.Infinite ∧4      (∀ (a : ↑A), IsLeast (Nat.totient ⁻¹' {↑a}) (n a)) ∧5        Filter.Tendsto (fun a => ↑(n a) / ↑↑a) Filter.atTop Filter.atTop

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