The board / number theory / #412
Erdős Problem #412
OPENdatabase updated 2025-08-31
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
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Let \(σ_1(n)=σ(n)\), the sum of divisors function, and \(σ_k(n) = σ(σ_{k-1}(n))\). Is it true that, for every \(m, n ≥ 2\), there exist some \(i, j\) such that \(σ_i(m) = σ_j(n)\)?
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open. The authoritative wording is on erdosproblems.com/412.Prizenone
Topicsnumber theory, iterated functions
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/412
Attempts
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Independently proved computationally that the sigma-orbits of 2 and 5 have no common value at most 10^342, extending their published 10^200 separation; no uniform invariant was found, and the next fre
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