Calculate the MU-numbers The first two MU-numbers are 2 and 3.  Every other MU-number is the smallest number not yet appeared that can be expressed as the product of two earlier distinct MU-numbers in exactly one way.

Here are the first 10

2, 3, 6, 12, 18, 24, 48, 54, 96, 162


Task

Given a positive number calculate and output the nth MU-number.

This is a code-golf competition so you should aim to make your source code as small as possible.

OEIS A007335
Pyth, 22 21 bytes
@u+Gfq2l@GcLTGheGQhB2

Try it online. Test suite.
0-indexed.
Explanation
@u+Gfq2l@GcLTGheGQhB2Q    Implicitly append Q and read+eval input to it.
                  hB2     Take the list [2, 2 + 1].
 u               Q        Put the list in G and apply this Q times:
               eG           Get last number in G.
              h             Add one.
    f                       Starting from that, find the first T such that:
          cLTG                Divide T by each of the numbers in G.
        @G                    Find the quotients that are also in G.
       l                      Get the number of such quotients.
     q2                       Check that it equals 2.
  +G                        Append that T to G.
@                    Q    Get the Q'th number in G.