Smooth factorisation

Let's define a smooth factorization of n! as $n!=f_1\times f_2\times \cdots \times f_n$ with :
$f_i\le f_{i+1}$
$f_n=\text{the largest prime factor of}n!$

Examples:
$13!=2\times 3\times 3\times 5\times 5\times 6\times 6\times 6\times 7\times 8\times 8\times 11\times 13$
$=3\times 4\times 4\times 4\times 5\times 5\times 6\times 6\times 6\times 6\times 7\times 11\times 13$
$14!=4\times 4\times 4\times 4\times 4\times 5\times 5\times 6\times 7\times 7\times 9\times 9\times 11\times 13$

Find the last (in numeric lexicographic order) smooth factorization of 28!

Answer format: Comma separated list of factors.
Example: 5,6,6,6,6,6,6,6,6,7,7,8,8,10,10,11,13,17,19 // For 19!

[My timing: 70 sec]