Suppose that p1, p2, p3 are distinct primes and that n, k Z+ with n =

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Suppose that p1, p2, p3 are distinct primes and that n, k ∈ Z+ with n = p15p23p3k. Let A be the set of positive integer divisors of n and define the relation R on A by x R y if x (exactly) divides y. If there are 5880 ordered pairs in R, determine k and | A |.
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