The smallest two perfect numbers $n=6$ and $m=28$ satisfy
$$
\frac{m}{n+1} = 2^k
$$

with $k=2.$

Question: Are there more pairs of perfect numbers $n,m$  with $n < m$
and such that

$$
\frac{m}{n+1} = 2^k
$$

for some positive integer $k>0.$