Erdős problem 51

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 $a → ∞$ ?

Sources

The source's own material, retained exactly.

1 retained statement36c6d0fef71a

FormalConjectures/ErdosProblems/

51.lean

Retained formal statement1 of 1

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 $a → ∞$ ?

FormalConjectures/ErdosProblems/51.leanErdos51.erdos_515 linesExact file

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

OpenStatement only, no proof