Hi Codeforces :P.

I'm trying to solve a problem about how many divisors has a Number.

In the Solutions Statements say that:

if we obtain only the factors of the number up to cube root of N.

then we obtain N = C*(factorization_of_N_up_to_cube_root)

and C can be only 1 or prime or prime*prime.

but i dont understand why.

Can see the entire explanation in the Presentation of the Solution, Problem F.

Presentation of Solutions|Problem F

I would greatly appreciate your help.