The page has "Primorials", but does not have "Factorials", I try to take the

factorials.

Also, I try the

highly abundant numbers, since they are the numbers whose sigma function sets record, and sigma function is highly related to Aliquot sequences.

Besides, there are also interesting bases: 102 and 138, see

https://oeis.org/A098009, they set record for the length of Aliquot sequences.

Finally, not only the Lehmer five, there are also other numbers less than 1000 which is conjectured to have an infinite, aperiodic, aliquot sequence: 306, 396, 696, 780, 828, 888, 996, which have the same trajectories as the Lehmer five.