Erdős problem 1064

Let $ϕ(n)$ be the Euler's totient function, then the $n$ satisfies $ϕ(n)>ϕ(n - ϕ(n))$ have asymptotic density 1. Reference: [LuPo02] Luca, Florian and Pomerance, Carl, On some problems of {M}\polhk akowski-{S}chinzel and {E}rdős concerning the arithmetical functions {$\phi$} and {$\sigma$}. Colloq. Math.