IMC 2014 Problem 4

Let $n>6$ be a perfect number, and let $n=p_1^{e_1}\cdot\cdot\cdot p_k^{e_k}$ be its prime factorisation with $1<p_1<\dots <p_k$ . Prove that $e_1$ is an even number. A number $n$ is perfect if $s(n)=2n$ , where $s(n)$ is the sum of the divisors of $n$ .

(Proposed by Javier Rodrigo, Universidad Pontificia Comillas)