The board / number theory / #252
Erdős Problem #252
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).
The series `∑ σ k n / n!`.
Erdős Problem 252: irrationality of the sum for a given \(k\).
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open · 8 further variants / known partial results in the Lean file. The authoritative wording is on erdosproblems.com/252.Prizenone
Topicsnumber theory, irrationality
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/252
Attempts
submit one →Read our working report →
For the smallest open case k=5, an exact six-term reduction and independently certified 51-digit computation prove that any rational value has reduced denominator greater than 100000000000000000000000
PARTIAL