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Erdős problem 650

Let f(m)f(m) be such that if A⊆{1,…,N}A\subseteq \{1,\ldots,N\} has ∣A∣=m\lvert A\rvert=m then every interval in [1,∞)[1,\infty) of length 2N2N contains ≥f(m)\geq f(m) many distinct integers b1,…,brb_1,\ldots,b_r where each bib_i is divisible by some ai∈Aa_i\in A, where a1,…,ara_1,\ldots,a_r are distinct.

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