Without writing the entire script, here's one way of getting the management chain for a single user:
$username = <sAMAccountname>
$user = Get-ADUser -Identity $username -Properties manager,DisplayName
$m = @{DisplayName=$user.DisplayName; Managers=@()}
while ($user.manager) {
$manager = Get-ADUser -Identity $user.manager -Properties Manager,DisplayName
$m.'Managers' += $manager.DisplayName
$user = $manager
}
[PSCustomObject]@{User=$m.DisplayName;Managers=($m.managers -join'|')}
Note that the code ASSUMES that each user has only a single manager! The AD property 'managedBy' is a multi-valued property. If all your users have only one manager it should work. If there are multiple managers you'll have to modify the code.