KöMaL 2015 A635

Show that for every positive real number $c>0$ there is a positive integer $n$ such that $\varphi\big(\sigma(n)\big)>cn$ . (For an arbitrary postive integer $k$ , $\varphi(k)$ denotes the number of positive integers not exceeding $k$ that are co-prime with $k$ . $\sigma(k)$ is the sum of positive divisors of $k$ .)