IITB Practice Set: 30

Question

How many ordered pairs of positive integers $(a,b)$ are there such that $\text{lcm}(a,b) = n \text{ and gcd}(a,b) = 1?$
Express your answer in terms of the prime factorization of $n$, given as $n = p_1^{d_1} \dots p_t^{d_t}.$