erdos_418.variants.sigma

Erdős has shown that a positive density set of integers cannot be written as $\sigma(n) - n$. [Er73b] Erdős, P., _Über die Zahlen der Form $\sigma (n)-n$ und $n-\phi(n)$_. Elem. Math. (1973), 83-86.

theorem erdos_418.variants.sigma :
    ∃ (S : Set ℕ) (hS : S.HasPosDensity),
      S ⊆ { (σ 1 n - n : ℕ) | n }ᶜ

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