Erdős problem 825 · problems.science

Is there an absolute constant $C > 0$ such that every integer $n$ with $\sigma(n) > Cn$ is the distinct sum of proper divisors of $n$ ?

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825.lean

Retained formal statement1 of 2

Is there an absolute constant $C > 0$ such that every integer $n$ with $\sigma(n) > Cn$ is the distinct sum of proper divisors of $n$ ?

This has been solved in the affirmative by Larsen - in fact, for any $\epsilon>0$ there exists $L$ such that if $n$ has only prime divisors $>L$ and $\sigma(n)>(2+\epsilon)n$ then $n$ is the distinct sum of proper divisors of $n$ .

FormalConjectures/ErdosProblems/825.leanErdos825.erdos_8251 lineExact file

1True ↔ ∃ C, ∃ (_ : C > 0), ∀ (n : ℕ), ↑((ArithmeticFunction.sigma 1) n) > C * ↑n → ∃ s ⊆ n.properDivisors, n = s.sum id

SolvedStatement only, no proof

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