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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theorem erdos_51 : answer(sorry) ↔ ∃ A : Set ℕ, ∃ n : A → ℕ,
A.Infinite ∧
(∀ a : A, IsLeast (φ ⁻¹' {(a : ℕ)}) (n a)) ∧
Tendsto (fun a : A => (n a : ℝ) / (a : ℝ)) atTop atTop
