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