How many divisors

The number of divisors of a number $n$ in the form $n=\alpha_1 ^{p_1} *\alpha_2 ^{p_2} *...*\alpha_n ^{p_n}$ where $\alpha _1, \alpha _2 ... \alpha _n$ are prime numbers, is given by $N_d=(p_1+1)*(p_2+2)*...*(p_n+1)$ .

The way to write 30 minimizing the value of $n$ is $30=5*3*2 \rightarrow n=2^4*3^2*5=720$