I agree with Vincente, it's nearly impossible to help you if you just say "why doesn't this work?". We have no idea what you're trying to accomplish.
The only thing I can guess is that you can't get your dataase to update properly. If that's the case,
I'd change
$query = "update veckan set ('$week')";
to something like
$query = "UPDATE veckan set week='$week' WHERE id='$id'";
set week='$week' means set the fieldname in my database week to equal the variable $week. Otherwise, mysql doesn't know what to update. If you're fieldname isn't week, then you can just change that to whatever your field name is.
The WHERE id='$id' is so mysql knows which row to update. A field can have more than one row, so you have to let mysql know which field AND row you wan't to update. I'm assuming you have some kind of unique id field for each record.
Cgraz
P.S. I just saw your other post and it looks like you're just using UPDATE improperly. Take vincente's advice and look at the manual for the proper way to use the update command. http://www.mysql.com/doc/en/UPDATE.html