I need help with this question please!
Create a formula (using sigma, logs, floor function) that computes the exponent of any particular prime in the prime factorization of a given factorial.
we use the notation
exp(p, n!) = the exponent of prime p in the prime factorization of n!
Example: exp(5, 25!) = 6
A Simple Formula
For example, 625! contains 125 multiples of 5, 25 multiples of 25, 5 multiples of 125, and 1 multiple of 625, thus .
If you're actually going to use this in practice, the is not necessary. Since for , you only have to sum up to , but that doesn't make for as pretty of a formula.