OPEN
This is open, and cannot be resolved with a finite computation.
Let $\sigma_1(n)=\sigma(n)$, the sum of divisors function, and $\sigma_k(n)=\sigma(\sigma_{k-1}(n))$. Is it true that for all $n\geq 2$\[\lim_{k\to \infty} \sigma_k(n)^{1/k}=\infty?\]
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Formalised statement?
Yes
Related OEIS sequences:
A007497
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When referring to this problem, please use the original sources of Erdős. If you wish to acknowledge this website, the recommended citation format is:
T. F. Bloom, Erdős Problem #410, https://www.erdosproblems.com/410, accessed 2026-04-11
