the Aperture version sold at the App Store does not have a serial number. If it is asking for the serial number, it is a bug. This can happen, if the download was incomplete. Quite a few posters have reported this problem. So try, what necronym recommended. Reinstalling Aperture should fix this. It will be sufficient, to move Aperture to the Trash, you do not need to empty the Trash. Then sign into the AppStore again with exactly the same Apple ID that you used to buy Aperture. Reload the "Purchased" tab with ⌘R , if the "Install" button does not show and click "Install".