Erdős problem 409

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).

Sources

The source's own material, retained exactly.

13 retained statements36c6d0fef71a

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