Guy, Richard K., Unsolved problems in number theory. Third edition, Problem Books in Mathematics, Springer, New York (2004), xviii+437 pp.; doi:10.1007/978-0-387-26677-0. Section B11 "Solutions of $m\sigma(m)=n\sigma(n)$", pp. 101--102; the distinctness of $n\sigma(n)$ for squarefree $n$ and the belief that $x\sigma(x)=n$ has fewer than $n^{\epsilon/\ln\ln n}$ solutions for every $\epsilon>0$, perhaps fewer than $(\ln n)^c$, are on p. 102. Library home: Guy 2004.