Definition:Solid Number/Similar Numbers

Definition
Let $m$ and $n$ be solid numbers.

Let:
 * $m = p_1 \times p_2 \times p_3$ where $p_1 \le p_2 \le p_3$
 * $n = q_1 \times q_2 \times q_3$ where $q_1 \le q_2 \le q_3$

Then $m$ and $n$ are similar iff:
 * $p_1 : q_1 = p_2 : q_2 = p_3 : q_3$