Natural numbers large enough can be written as $ab+ac+bc$ for some $a,b,c>0$

In their paper On the representations of xy+yz+zx,xy+yz+zx, Exper. Math. 2000, 153-158, Borwein and Choi prove that only one other possible solution exists ($> 10^{11}$) and that cannot occur if we assume the Generalized Riemann Hypothesis.

This problem is closely connected to old problems on class numbers of imaginary quadratic fields, e.g. see the excerpt below from the Putnam collection by Kedlaya, Poonen, Vakil.