Let f: \mathbb{N} \rightarrow(0, \infty) satisfy \prod_{d \mid n} f(d)=1 for every n which is not prime. Determine the maximum possible number of n with 1 \leq n \leq 100 and f(n) \neq 1.
Let f: \mathbb{N} \rightarrow(0, \infty) satisfy \prod_{d \mid n} f(d)=1 for every n which is not prime. Determine the maximum possible number of n with 1 \leq n \leq 100 and f(n) \neq 1.