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 statement6 of 13

What is the density of $n$ which reach any fixed prime under the iteration $n\mapsto\phi(n) + 1$ ?

FormalConjectures/ErdosProblems/409.leanErdos409.erdos_409.parts.iii1 lineExact file

1∀ (p : ℕ), Nat.Prime p → ∀ (α : ℝ), {n | ∃ i, (fun x => x.totient + 1)^[i] n = p}.HasDensity α → α = sorry

OpenStatement only, no proof

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