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Erdős problem 51

Is there an infinite set A⊂NA \subset \mathbb{N} such that for every a∈Aa \in A, there is an integer n such that ϕ(n)=a\phi(n)=a, and yet if nan_a is the smallest such integer, then naa→∞\frac{n_a}{a} → \infty as a→∞a → ∞?

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FormalConjectures/ErdosProblems/

51.lean

Retained formal statement1 of 1

Is there an infinite set A⊂NA \subset \mathbb{N} such that for every a∈Aa \in A, there is an integer n such that ϕ(n)=a\phi(n)=a, and yet if nan_a is the smallest such integer, then naa→∞\frac{n_a}{a} → \infty as a→∞a → ∞?

FormalConjectures/ErdosProblems/51.leanErdos51.erdos_515 linesExact file
True ↔  ∃ A n,    A.Infinite ∧      (∀ (a : ↑A), IsLeast (Nat.totient ⁻¹' {↑a}) (n a)) ∧        Filter.Tendsto (fun a => ↑(n a) / ↑↑a) Filter.atTop Filter.atTop
OpenStatement only, no proof

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