Let $D_n$ be the product of all positive divisors of a positive integer $n.$ $\big($For example, $D_1 = 1$ and $D_4 = 1 \times 2 \times 4 = 8.\big)$

What is the smallest positive integer $n$ for which $D_n$ can be written as
$D_n = p^a \times q^b \times r^c \times s^d,$
where $p, q, r, s$ are four distinct prime numbers **and** $a,b,c,d$ are four distinct positive integers?

**Bonus 1:** Can you solve this for prime numbers $p$ , $q$ , $r$ , $s$ , $t$ and integers $a,b,c,d,e?$

**Bonus 2:** Can you generalize for $p_{1}, ...,p_{n},$ where all primes in the prime factorization are raised to different powers?

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