Erdős problem 1210 · problems.science

Let $A\subseteq [1,n)$ be a set of integers such that $(a,b)=1$ for all distinct $a,b\in A$ . Is it true that $\sum_{a\in A}\frac{1}{n-a}\leq \sum_{p < n}\frac{1}{p}+O(1)$ ?

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2 retained statements2415f78e850a

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FormalConjectures/ErdosProblems/

1210.lean

Retained formal statement2 of 2

In [Er80] he claims he "did not state this quite correctly" in [Er77c]. The problem in [Er77c] which Erdős is presumably referring to states that if $n < q_1 < \cdots < q_k\leq m$ is the set of primes in $(n,m]$ then $\sum \frac{1}{q_i-n} < \sum_{p < m-n}\frac{1}{p}+O(1)$ .

FormalConjectures/ErdosProblems/1210.leanErdos1210.erdos_1210.variants.er80_correction4 linesExact file

1True ↔2  ∃ C,3    ∀ (n m : ℕ),4      n < m → ∑ q ∈ Finset.Ioc n m with Prime q, 1 / (↑q - ↑n) < ∑ p ∈ Finset.range (m - n) with Prime p, 1 / ↑p + C

OpenStatement only, no proof

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