An interesting question! Did not know of Landau's function. Any partition with repeated sizes has the same LCM as if all the extra duplicates are replaced by ones. So at least partitions with repetition — except for ones — can be ignored. Yikes, this seems a Herculean task. Can anyone come up with reasonable upper or lower bounds, even? Or some kind of asymptotic bounds? Here is at least some relevant info: https://oeis.org/A000793. —Dan ----- . . . a reasonable way to evaluate Landau's function (A000793) at 2^16 = 65536. This is the maximum least common multiple of any partition of 65536; equivalently it is the maximum order of any element of Sym(65536). I am sure there are lots of shortcuts, that save one from enumerating all the partitions of 65536. Can anyone suggest one? . . . -----