Guy, Richard K., Unsolved problems in number theory, third edition, Problem Books in Mathematics, Springer (2004), xviii+437 pp.; B36 "Euler's totient function", printed p. 139: Erdős's question whether for every $\epsilon$ there is an $n$ with $\phi(n)=m$, $m<\epsilon n$, and $\phi(t)\ne m$ for all $t<n$, "perhaps there are many such $n$". Library home: Guy 2004.