Erdős problem 277

Is it true that, for every $c$ , there exists an $n$ such that $\sigma(n)>cn$ but there is no covering system whose moduli all divide $n$ ?

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1 retained statement36c6d0fef71a

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FormalConjectures/ErdosProblems/

277.lean

Retained formal statement1 of 1

Is it true that, for every $c$ , there exists an $n$ such that $\sigma(n)>cn$ but there is no covering system whose moduli all divide $n$ ?

This was answered affirmatively by Haight [Ha79].

FormalConjectures/ErdosProblems/277.leanErdos277.erdos_2771 lineExact file

1True ↔ ∀ (c : ℝ), ∃ n, ↑((ArithmeticFunction.sigma 1) n) > c * ↑n ∧ ∀ (m : StrictCoveringSystem ℤ), ∃ i, ↑n ∉ m.moduli i

SolvedStatement only, no proof