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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FormalConjectures/ErdosProblems/

409.lean

Retained formal statement13 of 13

If $n > 0$ , then the iteration $n\mapsto\phi(n) + 1$ necessarily reaches a prime.

FormalConjectures/ErdosProblems/409.leanErdos409.erdos_409.variants.termination1 lineExact file

1∀ (n : ℕ), 0 < n → ∃ i, Nat.Prime ((fun x => x.totient + 1)^[i] n)

TestStatement only, no proof

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