(programming required) In Example 9.31, we analyzed the number of ways to write a particular integer n as the product of primes. (Because the prime factorization of n is unique, the only difference...

(programming required) In Example 9.31, we analyzed the number of ways to write a particular integer n as the product of primes. (Because the prime factorization of n is unique, the only difference between these products is the order in which the primes appear.) Write a program, in a language of your choice, to compute the number xn of ways we can write a given number n as p1 · p2 · · · pk , where each pi is prime. For what number n ≤ 10,000 is xn the greatest?