Is it true that, for every $c$ , there exists an $n$ such that $σ (n) > c n$ but there is no covering system whose moduli all distinct divisors of $n$ (which are $> 1$ )?

Worked, still open.

number theory · solved · formalized (Lean) · 0 attempts

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vela registry pull vfr_37aec80d874a0239

vela reproduce examples/erdos-problems

formal

AMS 11 · solved (literature)

theorem erdos_277 :
   answer(True) ↔ ∀ c : ℝ, ∃ n : ℕ, (σ 1 n : ℝ) > c * n ∧
      ∀ (m : StrictCoveringSystem ℤ), ∃ i, (n : ℤ) ∉ m.moduli i

solved