Erdős problem 409 · problems.science

If $n > 1$ then the iteration $n\mapsto\sigma(n) - 1$ 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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13 retained statements2415f78e850a

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FormalConjectures/ErdosProblems/

409.lean

Retained formal statement11 of 13

Is it true that iterates of $n\mapsto\sigma(n) - 1$ always reach a prime?

FormalConjectures/ErdosProblems/409.leanErdos409.erdos_409.variants.sigma_prime_termination1 lineExact file

1sorry ↔ ∀ n > 1, ∃ i, Nat.Prime ((fun x => (ArithmeticFunction.sigma 1) x - 1)^[i] n)

OpenStatement only, no proof

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