X

3. Let n = pt¹ × p²² × × per, where r, all ei, 1 ≤ i ≤r, are natural numbers, and all pi, 1 ≤ i ≤r are

distinct primes. How many ordered pairs (u, v) of positive integers are there with the property that

lcm(u, v) = n, where lcm stands for least common multiple.