what is the logic to evaluate f(n,k) where f(n,k)= number of ways in which n can be written as the Product of k distinct positive integers.
For example, f(144,4) = 7. There are 7 ways in which 144 can be written as a product of 4 distinct positive integers:
144 = 1×2×4×18
144 = 1×2×8×9
144 = 1×2×3×24
144 = 1×2×6×12
144 = 1×3×4×12
144 = 1×3×6×8
144 = 2×3×4×6