erdos_825.variants.necessary_cond

Specification

Show that if the constant $C > 0$ is such that every integer $n$ with $\sigma(n) > Cn$ is the distinct sum of proper divisors of $n$, then we must have $C > 2$.

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Lean 4 Statement

theorem erdos_825.variants.necessary_cond (C : ℝ) (hC : 0 < C)
    (h : ∀ (n : ℕ) (_ : σ 1 n > C * n),
        ∃ s ⊆ n.properDivisors, n = s.sum id) :
    2 < C

ID: ErdosProblems__825__erdos_825.variants.necessary_cond

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