CAPT DEPARTS LGA WITH VOR OTS. VOR IS REQUIRED FOR COMPANY ENGINE OUT PROC.

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LGA CLRNC DELIVERY ISSUED A CLRNC TO TAKEOFF FROM LGA ON RWY 31 VIA THE LA GUARDIA ONE DEP. THE LGA VOR WAS OUT OF SERVICE AT THE TIME; AND WAS NOTED ON THE ATIS. TAKEOFFS FROM RWY 31 REQUIRE THAT EITHER THE LGA VOR BE IN SERVICE OR; THAT THE PETHS NDB BE IN SERVICE TO COMPLY WITH THE SINGLE ENGINE DEP PROC OFF RWY 31. AT THE TIME OF THE TAKEOFF THE PETHS NDB WAS NOTAMED OUT OF SERVICE. THE TAKEOFF AND FLT WERE NORMAL. I WAS NOTIFIED BY THE CHIEF PLTS OFFICE THAT ALL ACFT THAT TOOK OFF FROM LGA THAT DAY OFF OF RWY 31 WERE NOT IN COMPLIANCE WITH THE NAVAIDS REQUIRED FOR THE SINGLE ENGINE DEP. I BELIEVE THAT BOTH ATC AND THE AIRMEN MISSED THE NOTAM BECAUSE THERE ARE SO MANY NOTAMS TO READ THROUGH IT IS DIFFICULT TO PICK OUT THE THINGS THAT ARE TRULY IMPORTANT TO THE FLT. DURING AN ACFT TURN THE CAPT MAY ONLY HAVE A COUPLE OF MINUTES TO READ THROUGH A LENGTHY LIST OF NOTAMS IF THE FLT IS TO REMAIN ON SCHEDULE. MAKING NOTAMS EASIER TO READ; AND IF POSSIBLE; REDUCING THE NUMBER PRINTED WOULD HELP. IT IS A REAL CHALLENGE TO DETERMINE THE NOTAMS THAT WILL IMPACT THE FLT. I WILL REVIEW WITH RENEWED EFFORT FOR ANY POSSIBLE IMPACT ON THE FLT.