## Superperfect number

n is superperfect if $\sigma(\sigma(n))=2n$
• Show that if $n=2^q$ where $2^{q+1}+1$ is prime, then $n$ is superperfect
$\sigma(\sigma(2^q))=\sigma(2^{q+1}-1)$ etc., so this part is ok for me
• Show that every even superperfect number is of this form.
Need help on this part.