The least number k = a(n) > a(n-1) for which k!/(k+1)^m for increasing m's.

Terms

a(0) =1a(1) =5a(2) =11a(3) =23a(4) =35a(5) =39a(6) =44a(7) =47a(8) =59a(9) =71a(10) =79a(11) =89a(12) =119a(13) =143a(14) =179a(15) =239a(16) =359a(17) =479a(18) =629a(19) =671a(20) =719a(21) =1079a(22) =1119a(23) =1259a(24) =1343a(25) =1439a(26) =1889a(27) =2015a(28) =2159a(29) =2239