Even if to compute all set with only two elements, your algorithm is not able to get it.
24 = 2^3*3, by your formula, the number of sets are 4*2-1 = 7. In fact, it is {24}, {2, 12}, {3, 8}, {4, 6}, which is only 4.
:)

I am not going to pointing your mistake here. Anyway, read the question carefully.

I do not think this question is able to be solved by permutation and combination formula. Indeed, it is hard to solve it. In programming, we also consider complexity of an algorithm. Another bottleneck to this problem is that there may be about 1000,000 number to compute. Then how?
Think about it...