Explanation

In this question, we are given n in a form that is almost its prime factorization, which is . To determine the number of divisors sought, we essentially have to count different combinations of the factors. We can break down the possibilities by the number of prime factors used to form each divisor. We can't have any divisors of just one prime factor, because the question stipulates that we count "non-prime" divisors. In the case that our divisor has two factors, it could be , or , or , or , for a total of 4 possibilities. In the case that our divisor has three prime factors, it could be , or , or , for a total of 3 possibilities. The case that our divisor has four prime factors is out, because that equals n, and we have been told to exclude n. Therefore, we have 7 possibilities of the type described.

The correct answer is (B).