[math-fun] Landau's function of 2^16

I got an email from Claus Michael Ringel at the University of Bielefeld, asking me if I knew 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? (Of all the code snippets in the relevant page at A000793, all of them except one are clearly just enumerating partitions and comparing LCM's. But Charles Greathouse's PARI code is not doing anything like that, and I don't have a clue what it *is* doing.)