For a positive integer n, let P(n) be the product of the factors of n (including n itself). A positive integer n is called \mathit{deplorable} if n>1 and \log _n P(n) is an odd integer. How many factors of 2016 are deplorable?
For a positive integer n, let P(n) be the product of the factors of n (including n itself). A positive integer n is called \mathit{deplorable} if n>1 and \log _n P(n) is an odd integer. How many factors of 2016 are deplorable?