The board / number theory / #1060
Erdős Problem #1060
OPENdatabase updated 2025-09-28
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
The conjecture is about the function \(f(n)\) which counts the number of solutions to \(k\sigma(k)=n\), where \(\sigma(k)\) is the sum of divisors of \(k\). The first bound is that \(f(n)\) grows slower than any power of \(n^(\frac{1}{\log\log n})\). The second bound is that \(f(n)\) is at most a power of \(\log n\).
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open · 1 further variant / known partial result in the Lean file. The authoritative wording is on erdosproblems.com/1060.Prizenone
Topicsnumber theory
Statement in LeanFormal Conjectures
Solution in Leanno
OEISA327153
Original pageerdosproblems.com/1060
Attempts
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Proved the exact powerful-core bijection, improved the general located exponent constant from log(3)/3 to log(2)/2 for every odd target, certified f(n)<=5 through 10^14 and f(n)<=1 for odd n through 1
PARTIAL