Inspired with this [PROBLEM](http://math.stackexchange.com/questions/474899/divisors-of-qkpr) I am interested in those natural numbers that the set of their divisors can be partitioned into two sets with equal product. For example we can decompose divisors of $8$ into $\lbrace 1,8\rbrace$ and $\lbrace 2,4\rbrace$. Is the sequence of this numbers well-known? Is there any characterization for them ? Any suggestion would be helpful.