Distributive factorials

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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