Erdős problem 18 · problems.science

Conjecture 1. Are there infinitely many practical numbers $m$ such that $h(m) < (\log \log m)^{O(1)}$ ?

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11 retained statements2415f78e850a

FormalConjectures/ErdosProblems/

18.lean

Retained formal statement2 of 11

Vose's Theorem. Vose proved the existence of infinitely many practical numbers $m$ such that $h(m) \ll (\log m)^{1/2}$ . This gives a positive answer to a weaker form of Conjecture 1.

FormalConjectures/ErdosProblems/18.leanErdos18.erdos_18_vose1 lineExact file

1∃ C, 0 < C ∧ ∃ᶠ (m : ℕ) in Filter.atTop, m.IsPractical ∧ ↑(Erdos18.practicalH m) < C * Real.log ↑m ^ (1 / 2)

SolvedStatement only, no proof

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