I know there are a few sync tools available in linux (I use openSuse OS btw), but I think they all do a pure sync and I am looking more for a backup function which is not synced (I could be mistaken). My computer hard disk is not so big, so ideally, I will put a file on my computer, sync, and be able to delete it on pc, while it stays on the hard disk. Is this at all possible in an automated way? It would make life so much easier... 
Automatic sync/backup that adds files to hard disk and keeps when removed
backup;synchronization