n t champion greatest prime factor of n^n + (n+1)^(n+1) 1 1 1 5 2 2 1 31 3 3 1 283 4 5 2 743 5 7 2 1600069 6 9 2 60042893 7 11 2 7438489991 8 14 2 61215157711 9 16 6 34041259347101651 10 18 3 6564253087266573169 11 19 4 22022174223585405703 12 21 2 69454092876521107983605569601 13 28 5 2360926164108571968813424783598971267 14 30 3 462605180698333957063188362720170172617217 15 33 4 14645575916792712592989131451003587034531413111 16 34 5 214236369415820799335832514547376967536187180963 17 37 2 1738879354765590249997542180390437704844184626147297 18 38 2 50009264964386795654135450172347199168195157319853468136631 19 52 5 39318552440214128278964884183562383661720239682442863098386411659849020310819527 20 54 3 993373072395059781023811613088852200937500386254894739216433419160648248035351936869397 21 55 3 867446719620668037689585325208425832087771600992531364110345252530282349332075240367793991 22 61 6 82961696113574647341918188297914238104033946299546480670188540918936855593836971213978175982479 23 62 6 96537621564272531306729692742899161385224831998018318412997475961045353676055330508383135030969 24 67 3 285078410341753132459059192693688035295447601955545063577435614563546047564703015937194371717881912809 25 70 7 47895133978387026920379629799932301414225993175767265205336987619070868582781561365798038312409606650349299 26 82 7 30642016713988874911608793345560398381708316917718994876203375643193752674857095491938078649931811446237837149867168293003423 27 85 5 1942838521702002984149249225314874319418576185307523490181852213695897740202674835170128332434880860124841385067117822636048691230458672454574092173339 28 90 2 16550031973035203923895326531423889447610817753390927205293872313295547200424066106802421592407404800537852404572681269524379305523361563701440471782282842382127662469 29 97 2 38945466765291042209055970129718121120464539084184978565545257723720144066541167031262774865604468021885376735179981436729991983957214830952373266239140346393506761921248959 above here , champions all determined t = OMEGA = the number of prime powers which divide n^n + (n+1)^(n+1) N.B. : n is from A056788 , not this sequence 98 * c192 This c192 could theoretically break into a p19 and a p173 , or etc. 100 11 8761479153664911000092939809409655200416259013725096941610844426019102582163273173363393769566266241396033883062679448108849683468026969421555512665960973546940988184081270355813 104 3 2645962755790815809561658972564447022992662892312648046380656243200093860681079805314608221345025689458999493693782089694320726702594034648703303990052511258194329045855182195981267445065743600881706693527477 110 c215 111 c218 112 c214 113 c227 114 c235 115 c221 116 5 81795907785621042774209081913750051065233180202388224036654890654011406427446341581386757393206110031180913570624075324729715280374418823104624062739781130502095196886430318241458949906404024568268325587769447903127 117 c233 119 c244 120 c239 121 c246 above here , carefully examined for potential champions ; I think 110 and 112 are also out by trial division to 10^7 or 10^8