Thaaaaaank you very much for your help. I will show you my solution:

So we use induction on the number of prime numbers appears in

;

If we have only one prime, then

and the divisors of

are

. Hence the number of divisors of

is

.

Inductive Step: Suppose that

contains

prime numbers, and the statement is true for

. i.e

and the number of divisors of

is

Our goal is to show that the statement is true for

which contain

prime numbers.

We have

. Hence

By inductive hypothesis, the number of divisors of

is

and we know that the number of divisors of

is

. So, the number of divisors of

is

which is

This is my solution. If there is any mistakes or comments please guide me. Thank you again