Guy, Richard K., Unsolved problems in number theory, third edition, Problem Books in Mathematics, Springer (2004), xviii+437 pp.; B41 "Iterations of $\phi$ and $\sigma$", printed p. 148: the third of six statements on the iterates $\sigma^k(n)$ that [EGPS90] "are unable to prove or disprove", "for every $n>1$, $(\sigma^k(n))^{1/k}\to\infty$ as $k\to\infty$?". Library home: Guy 2004.