Erdős problem 768

Let $A(x)$ count $n \le x$ such that every prime $p \mid n$ has a divisor $d > 1$ of $n$ with $d \equiv 1 \pmod p$. Erdos asked whether $A(x)/x = \exp(-(c+o(1))\sqrt{\log x}\log\log x)$. It does, with $c = 1/(2\sqrt{\log 2})$.