Erdős problem 859 · problems.science

The density of the divisor sum set is asymptotically equivalent to $c_1 / \log(t)^{c_2}$ .

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4 retained statements2415f78e850a

FormalConjectures/ErdosProblems/

859.lean

Retained formal statement2 of 4

A weaker version of the problem proved by Erdos: The density dₜ of DivisorSumSet (t : ℕ) is bounded from below by 1 / log (t) ^ c₃ and from above by 1 / log (t) ^ c₄ for some positive constants c₃ and c₄.

FormalConjectures/ErdosProblems/859.leanErdos859.erdos_859.variants.erdos_upper_lower_bounds5 linesExact file

1∃ c₃ > 0,2  ∃ c₄ > 0,3    ∃ t₀,4      ∀ᶠ (t : ℕ) in Filter.atTop,5        ∃ dₜ, (Erdos859.DivisorSumSet t).HasDensity dₜ ∧ 1 / Real.log ↑t ^ c₃ < dₜ ∧ dₜ < 1 / Real.log ↑t ^ c₄

SolvedStatement only, no proof

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