Erdős problem 410 · problems.science

Let $σ_1(n) = σ(n)$ , the sum of divisors function, and $σ_k(n) = σ(σ_{k-1}(n))$ .

Sources

Browse retained paths and inspect the exact material available for this Problem.

1 retained statement2415f78e850a

Open selected source

FormalConjectures/ErdosProblems/

410.lean

Retained formal statement1 of 1

Let $σ_1(n) = σ(n)$ , the sum of divisors function, and $σ_k(n) = σ(σ_{k-1}(n))$ .

Is it true that $\lim_{k → ∞} σ_k(n)^{\frac 1 k} = ∞$ ?

This is problem (iii) from Erdos, Granville, Pomerance, Spiro "On the normal behavior of the iterates of some arithmetical functions" (page 169 of the book "Analytic Number Theory", 1990).

FormalConjectures/ErdosProblems/410.leanErdos410.erdos_4101 lineExact file

1True ↔ ∀ n > 1, Filter.Tendsto (fun k => ↑((⇑(ArithmeticFunction.sigma 1))^[k] n) ^ (1 / ↑k)) Filter.atTop Filter.atTop

OpenStatement only, no proof

Sources

Search problems.science