How many ordered pairs of positive integers \(1 \leq k \leq n \leq 50\) are there, such that \(k\) divides \(n\), and

\[ \left(\frac{n}{k}\right)! = \frac{n!}{k!} \quad ? \]

**Details and assumptions**

For an **ordered pair of integers** \((a,b)\), the order of the integers matter. The ordered pair \((1, 2)\) is different from the ordered pair \((2,1) \).

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