76 elements of N below 10^9 are known, namely
#1: 5 (2^2+1) #2: 6 #3: 17 (2^4+1) #4: 31 (2^5-1) #5: 33 (2^5+1) #6: 63 (2^6-1) #7: 127 (2^7-1) #8: 129 (2^7+1) #9: 171 (2^9+1)/3 #10: 257 (2^8+1) #11: 511 (2^9-1) #12: 683 (2^11+1)/3 #13: 2047 (2^11-1) #14: 2731 (2^13+1)/3 #15: 2979 (2^15+1)/11 #16: 3277 (2^14+1)/5 #17: 3641 (2^15+1)/9 #18: 8191 (2^13-1) #19: 28197 (2^24-1)/595 #20: 43691 (2^17+1)/3 #21: 48771 (2^21+1)/43 #22: 52429 (2^18+1)/5 #23: 61681 (2^20+1)/17 #24: 65537 (2^16+1) #25: 85489 (2^26+1)/785 #26: 131071 (2^17-1) #27: 174763 (2^19+1)/3 #28: 178481 (2^23-1)/47 #29: 233017 (2^21+1)/9 #30: 253241 (2^26+1)/265 #31: 256999 (2^29-1)/2089 #32: 486737 (2^29-1)/1103 #33: 524287 (2^19-1) #34: 704093 (2^30+1)/1525 #35: 784899 (2^27+1)/171 #36: 838861 (2^22+1)/5 #37: 1016801 (2^25+1)/33 #38: 1082401 (2^25-1)/31 #39: 1609167 (2^36-1)/42705 #40: 1657009 (2^27+1)/81 #41: 1838599 (2^27-1)/73 #42: 1965379 (2^36-1)/34965 #43: 2304167 (2^29-1)/233 #44: 2792907 (2^36-1)/24605 #45: 2796203 (2^23+1)/3 #46: 3033169 (2^29+1)/177 #47: 3303821 (2^30+1)/325 #48: 3605429 (2^34+1)/4765 #49: 3705353 (2^35+1)/9273 #50: 6700417 (2^32+1)/641 #51: 7949043 (2^36-1)/8645 #52: 8727391 (2^35-1)/3937 #53: 9335617 (2^36+1)/7361 complete up to n=10^7 #54: 12576771 (2^33+1)/683 #55: 13788017 (2^33-1)/623 #56: 15790321 (2^28+1)/17 #57: 19173961 (2^27-1)/7 #58: 21225581 (2^42+1)/207205 #59: 24214051 (2^35+1)/1419 #60: 25080101 (2^34+1)/685 #61: 25781083 (2^37+1)/5331 #62: 53353631 (2^33-1)/161 #63: 102964687 (2^45-1)/341713 #64: 120296677 (2^38+1)/2285 #65: 164511353 (2^41-1)/13367 #66: 169533009 (2^45+1)/207537 #67: 201302019 (2^39+1)/2731 #68: 207207011 (2^45+1)/169803 #69: 240068041 (2^38+1)/1145 #70: 256957153 (2^45-1)/136927 #71: 464955857 (2^46+1)/151345 #72: 598781009 (2^42+1)/7345 #73: 616318177 (2^37-1)/223 #74: 715827883 (2^31+1)/3 #75: 905040953 (2^43-1)/9719 #76: 993089953 (2^54+1)/18139745 complete up to n=10^9 for pmorder < 200
Note that the MAD numbers larger than 3 are precisely the numbers not divisible by 3 on this list.
There is also information on a rectangular board.