Another Divisors Problem

Let DnD_n be the product of all positive divisors of a positive integer n.n. (\big(For example, D1=1D_1 = 1 and D4=1×2×4=8.)D_4 = 1 \times 2 \times 4 = 8.\big)

What is the smallest positive integer nn for which DnD_n can be written as Dn=pa×qb×rc×sd,D_n = p^a \times q^b \times r^c \times s^d, where p,q,r,sp, q, r, s are four distinct prime numbers and a,b,c,da,b,c,d are four distinct positive integers?


Bonus 1: Can you solve this for prime numbers pp , qq , rr , ss , tt and integers a,b,c,d,e?a,b,c,d,e?
Bonus 2: Can you generalize for p1,...,pn,p_{1}, ...,p_{n}, where all primes in the prime factorization are raised to different powers?

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