Generalise perfect numbers
PowerShell, 95 92 87 bytes
-8 bytes thanks to mazzy!
This takes two parameters, m and k, and calculates all (m,k) perfect numbers (up to the maximum for a 64-bit signed integer).

param($m,$k)for(;$n=++$x){1..$m|%{$a=0;1..$n|%{$a+=$_*!($n%$_)};$n=$a}
,$x*!($a-$k*$x)}

Try it online!