I received the question a couple of times so I decided to answer it here:
You cannot install September 2013 PU (public update) on top of August 2013 CU because August 2013 CU already includes September 2013 PU.
PUs are more intensively tested than CUs. Code changes done for September PU are also included in August CU. But September PU released one month later due to additional testing done on the public update.
More Details on CUs and PUs can be found here: