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Erdős problem 12

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Let A⊂NA \subset \mathbb{N} be infinite with no distinct a,b,c∈Aa, b, c \in A such that a∣(b+c)a \mid (b + c) with b,c>ab, c > a. Can ∣A∩[1,N]∣/N|A \cap [1, N]|/\sqrt{N} have positive lower limit? Must every such AA fall below N1−cN^{1-c} infinitely often?

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10 retained statements36c6d0fef71a

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FormalConjectures/ErdosProblems/

12.lean

Retained formal statement3 of 9

Let AA be an infinite set such that there are no distinct a,b,c∈Aa,b,c \in A such that a∣(b+c)a \mid (b+c) and b,c>ab,c > a. Is it true that ∑n∈A1n<∞∑_{n \in A} \frac{1}{n} < \infty?

FormalConjectures/ErdosProblems/12.leanErdos12.erdos_12.parts.iii1 lineExact file
sorry ↔ ∀ (A : Set ℕ), Erdos12.IsGood A → Summable fun n => 1 / ↑↑n
OpenStatement only, no proof