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erdos_392.variants.lower

Specification

If we change the condition to $a_t \leq n$ it can be shown that $$ A(n) = n - \frac{n}{\log n} + o\left(\frac{n}{\log n}\right) $$

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Lean 4 Statement 
theorem erdos_392.variants.lower (A : ℕ → ℕ)
    (hA : ∀ n > 0, IsLeast
      { t + 1 | (t) (_ : ∃ a : Fin (t + 1) → ℕ, (n)! = ∏ i, a i ∧
        Monotone a ∧ a (Fin.last t) ≤ n) } (A n)) :
    (fun (n : ℕ) => (A n - n + n / Real.log n : ℝ)) =o[atTop] fun n => n / Real.log n
ID: ErdosProblems__392__erdos_392.variants.lower
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