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Erdős problem 319

What is the size of the largest A⊆{1,…,N}A\subseteq\{1, \dots, N\} such that there is a function δ:A→{−1,1}\delta : A \to \{-1, 1\} such that ∑n∈Aδnn=0 \sum_{n\in A} \frac{\delta n}{n} = 0 and ∑n∈A′δnn≠0 \sum_{n\in A'}\frac{\delta n}{n} \neq 0 for all non-empty A′⊊AA'\subsetneq A.

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FormalConjectures/ErdosProblems/

319.lean

Retained formal statement1 of 5

What is the size of the largest A⊆{1,…,N}A\subseteq\{1, \dots, N\} such that there is a function δ:A→{−1,1}\delta : A \to \{-1, 1\} such that ∑n∈Aδnn=0 \sum_{n\in A} \frac{\delta n}{n} = 0 and ∑n∈A′δnn≠0 \sum_{n\in A'}\frac{\delta n}{n} \neq 0 for all non-empty A′⊊AA'\subsetneq A.

FormalConjectures/ErdosProblems/319.leanErdos319.erdos_3197 linesExact file
∀ (N : ℕ),  IsGreatest    {x |      ∃ A,        ∃ (_ : A ⊆ Finset.Icc 1 N) (_ :          ∃ δ, ∑ n ∈ A, ↑↑(δ n) / ↑n = 0 ∧ ∀ A' ⊂ A, A'.Nonempty → ∑ n ∈ A', ↑↑(δ n) / ↑n ≠ 0), A.card = x}    sorry
OpenStatement only, no proof

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