The board / number theory / #825
Erdős Problem #825
PROVED LEANdatabase updated 2026-08-23
The statement as posed is true, and a proof exists. A solution has also been checked by machine, in Lean.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
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 \(n\).
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved · 1 further variant / known partial result in the Lean file. The authoritative wording is on erdosproblems.com/825.Prize$25
Topicsnumber theory, divisors, unit fractions
Statement in LeanFormal Conjectures
Solution in Leanyes
Original pageerdosproblems.com/825
Attempts
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