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Erdős problem 409

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If n>1n > 1 then the iteration n↦σ(n)−1n\mapsto\sigma(n) - 1 necessarily reaches a prime. Note: this is open — it is not clear that the σ iteration always terminates, since it is non-decreasing (unlike the φ iteration which is strictly decreasing).

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FormalConjectures/ErdosProblems/

409.lean

Retained formal statement12 of 13

If n>1n > 1 then the iteration n↦σ(n)−1n\mapsto\sigma(n) - 1 necessarily reaches a prime. Note: this is open — it is not clear that the σ iteration always terminates, since it is non-decreasing (unlike the φ iteration which is strictly decreasing).

FormalConjectures/ErdosProblems/409.leanErdos409.erdos_409.variants.sigma_termination1 lineExact file
∀ n > 1, ∃ i, Nat.Prime ((fun x => (ArithmeticFunction.sigma 1) x - 1)^[i] n)
OpenStatement only, no proof