I'd probably run the whole collection through Select-Object -unique to generate and store a list of unique server names.
I'd then enumerate those. For each server name, I'd select – from the original collection and using Where-Object – all objects having the current server name. I'd then further Where-Object that to get just the objects with localadmins, and send that to Measure-Object.
If the resulting Measure object had a count of zero, I'd output the current server name.
Vaguely, because I haven't had coffee yet...
$coll = do whatever you do to populate the collection
$names = $coll | select-object -prop server -unique | select -expand server
ForEach ($name in $names) {
$count = $coll | Where server -eq $name | Where member -eq localadmins | measure
If ($count.count -eq 0) {
Write $name
}
}
