Japt, 14 bytes

k â £è_¶X Vn w 

Try it

I'm new to Japt so I'm sure this can be golfed way more. Particularly, I have n w to sort the occurrences in descending order but I think there's a shorter way, and I'm not sure â £è_¶X is the best way to get the number of occurrences of each element in an array. Please suggest any ways to improve the score!

Japt, 8 bytes

-6 thanks to @Shaggy

k ü mÊñn 

Try it

k ü mÊñn k Get the prime factors of the input ü Group the factors to lists of the same element mÊ Map each group to its length ñn Sort them in descending order