Under an anti-concentration hypothesis excluding energy-saturating divisor ladders, the orbit length a(x) satisfies a(x) ≍ x / log x.
The concentra- tion of divisors.Inventiones Mathematicae, 232:1019–1067, 2023
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The Divisor Function along a Deterministic Orbit and the Emergence of Ladders
Under an anti-concentration hypothesis excluding energy-saturating divisor ladders, the orbit length a(x) satisfies a(x) ≍ x / log x.