AN A320 DIVERTED DUE APU FIRE WARNING AND PRECAUTIONARY DISCHARGE OF FIRE EXTINGUISHER. CONTRACT MAINT ENTERED A WRONG MEL REF IN LOGBOOK.

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WE WERE IN CRUISE FLT NW OF ZZZ (APPROX 100-150 MI) WHEN WE RECEIVED AN 'APU LOOP A FAULT.' THE APU WAS OFF AND THE MESSAGE WAS A CREW AWARENESS ONLY. (NO ACTION.) ABOUT 2 MINS LATER; THE APU FIRE BUTTON ILLUMINATED RED WITH NO ECAM. FOLLOWING THE FCOM PROC; I PUSHED THE APU FIRE BUTTON OUT AND ARMED THE SQUIB. AFTER 10 SECONDS; I DISCHARGED THE BOTTLE AND THE LIGHT INDICATED 'DISCHARGED.' AFTER CONTACTING MAINT CTL AND DISCUSSING OUR SIT WITH THEM (AT THIS POINT WE WERE FAIRLY CERTAIN IT WAS AN INDICATION PROB); WE DECIDED TO GO TO ZZZ SINCE THE APU FIRE LIGHT WAS STILL ON AND THE FCOM SAID TO LAND ASAP. THE ARR INTO ZZZ WAS UNEVENTFUL AND WE DID THE OVERWT LNDG CHKLIST PER THE QRH. UPON ARR AT THE GATE; I ENTERED THE OVERWT LNDG AND THE APU FIRE INDICATION IN THE MAINT LOG. CONTRACT MAINT DID THE REQUIRED INSPECTIONS AND ENTERED 3 MEL'S IN THE BOOK. THEY WERE MEL #49-10-01 APU INOP; #26-13-01-3 APU FIRE DETECTION SYS INOP; AND #26-22-01-2 APU AGENT DISCHARGE LIGHT INOP -- WHICH WAS ENTERED AND THE REQUIRED MAINT ACTIONS WERE PERFORMED. AFTER MAINT CTL VERIFIED ALL REQUIREMENTS AND INSPECTIONS WERE COMPLIED WITH; THE LOGBOOK WAS SIGNED OFF AND WE MADE AN UNEVENTFUL TRIP TO ZZZ1. I WOULD LIKE TO ADD THAT ACCORDING TO CONTRACT MAINT; IT APPEARED THE SQUIB DID NOT DISCHARGE INTO THE APU EVEN THOUGH THE COCKPIT INDICATIONS SAID IT DID. ON THE TRIP TO ZZZ1; I NOTICED THAT CONTRACT MAINT ENTERED MEL 26-22-01-2 IN THE SUMMARY COLUMN AS 'APU FIRE EXTINGUISHING SYS INOP' WHICH IS ACTUALLY MEL 26-22-0. I BELIEVE IN MY RUSH TO GET THE PAX TO THEIR ORIGINAL DEST I MISSED THE INCORRECT WRITE-UP IN THE MAINT LOG. GOING FORWARD; I WILL BE MORE DILIGENT TO ENSURE CORRECT ENTRIES.