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Discrete Mathematics Level 3

Let \(n\) be a natural number (positive integer) and \(m\) be the number of distinct prime divisors of \(n\). For example, if \(n = 12 = 2^2 \cdot 3\), then \(m = 2\). In how many ways can \(n\) be expressed as a product of two relatively prime natural numbers?

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