erdos_319.variants.isBigO

Let $c(N)$ be the size of the largest $A\subseteq\{1, \dots, N\}$ such that there is a function $\delta : A \to \{-1, 1\}$ such that $$ \sum_{n\in A} \frac{\delta n}{n} = 0 $$ and $$ \sum_{n\in A'}\frac{\delta n}{n} \neq 0 $$ for all non-empty $A'\subsetneq A$. Find the simplest $g(N)$ such that $c(N) = O(g(N)).

theorem erdos_319.variants.isBigO (N : ℕ) (c : ℕ → ℝ)
    (h : ∀ N, IsGreatest
    { (#A : ℝ) | (A) (_ : A ⊆ Finset.Icc 1 N)
      (_ : ∃ δ : ℕ → ℤˣ, ∑ n ∈ A, (δ n : ℚ) / n = 0 ∧
        ∀ A' ⊂ A, A'.Nonempty → ∑ n ∈ A', (δ n : ℚ) / n ≠ 0) } (c N)) :
    c =O[atTop] (answer(sorry) : ℕ → ℝ)

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