Multifactorial and divisors

Number Theory Level 3

Fill in the blank.

$N$ has $3$ prime factors.

$N^2$ has $7!!$ positive divisors.

$N^3$ has $10!!!$ positive divisors.

$\text{\_\_\_\_}$ has $13!!!!$ positive divisors.

Note: You might want to read up the definition of multifactorials first.