Daily Challenge 7 - Factorial Decomposition

Today's challenge will require a bit of mathematical prowess. Those who were fans of the Project Euler challenges might have some fun with this one from user g964 from CodeWars:

The aim of this [challenge] is to decompose n!(factorial n) into its prime factors. Prime numbers should be in increasing order. When the exponent of a prime number is 1, don't print the exponent.

Examples:

n = 22; decomp(22) -> "2¹⁹ * 3⁹ * 5⁴ * 7³ * 11² * 13 * 17 * 19"
n = 25; decomp(25) -> "2²² * 3¹⁰ * 5⁶ * 7³ * 11² * 13 * 17 * 19 * 23"

Explanation:

n = 12; decomp(12) -> "2¹⁰ * 3⁵ * 5² * 7 * 11"
12! is divisible by 2 ten times, by 3 five times, by 5 two times and by 7 and 11 only once.

Thank you to CodeWars, who has licensed redistribution of this challenge under the 2-Clause BSD License!