When does :$\sigma(\sigma(2n))=\sigma(\sigma(n))$ and $\sigma(n)$ is sum divisors of the positive integer $n$? Is there someone who can show me When does: $$\sigma(\sigma(2n))=\sigma(\sigma(n))$$ where : $\sigma(n)$ denotes the sum of divisors of the positive integer $n$ ?
Note (1) : I came across this problem when I read some papers  about 
"Iterating of the sum divisors of sigma function ".
Note(2) :${\sigma}^{0}(n)=n$ and ${\sigma}^{m}(n)=\sigma({\sigma}^{m-1}(n))$ and $m \geq 1$
Thank you for any help!

$\sigma(2n)=3\times\sigma(n)$
if $m=\sigma(n)$
we should find $\sigma(3 m)=\sigma(m)$
$\sigma(3m)=4\times\sigma(m)$
then  $4\sigma(m)=\sigma(m)$
contradiction so there is no solution.
