The board / number theory / #859
Erdős Problem #859
OPENdatabase updated 2025-08-31
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).
`DivisorSumSet t` is the set of natural numbers `n` such that `t` can be represented as a sum of distinct divisors of `n`.
The density of the divisor sum set is asymptotically equivalent to \(c_1 / \log(t)^{c_2}\).
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/859.Prizenone
Topicsnumber theory, divisors
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/859
Attempts
submit one →Read our working report →
proved the exact finite-union/LCM reduction, derived the rigorous lower bound \(\liminf d_t\log t\ge ce^{-\gamma}\) from Weingartner's theorem (forcing any asymptotic exponent \(c_2\le1\)), and indepe
PARTIAL