Partitioning into Divisors

Discrete Mathematics Level pending

How many ordered triples of pairwise distinct, positive integers \( ( a, b, c) \) are there such that \( abc = 10^6 \)?

Details and assumptions

A set of values is called pairwise distinct if no two of them are equal. For example, the set \( \{1, 2, 2\} \) is not pairwise distinct, because the last 2 values are the same.

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