Problem Statement
Let $\sigma_1(n)=\sigma(n)$, the sum of divisors function, and $\sigma_k(n)=\sigma(\sigma_{k-1}(n))$. Is it true that\[\lim_{k\to \infty} \sigma_k(n)^{1/k}=\infty?\]
Categories:
Number Theory Iterated Functions
Progress
This is discussed in problem B9 of Guy's collection [Gu04].Source: erdosproblems.com/410 | Last verified: January 15, 2026