2023-05-30

Counting integer divisors

tags: [dev][mathematics][python][discrete-mathematics]

TL&DR: Although I’ve been using Python for years, its set notation still amazes me for its expressiveness. In this case to count integer divisors, given a specific predicate.

Context

This semester I’m doing a course on Discrete Mathematics. I had an exercise to count integer divisors of a given number, which weren’t divisible by another given number.

To verify my reply, which involved a bit more of analysis, Python enabled me to write a quick script that could do it.

I’ll link up my proper solution in Portuguese at a later date.

The question

Count the number of integer divisors of 37800, which aren’t divisible by 6.

The script

n = 37800
k = 6
p = (lambda i, n, k: n % i == 0 and i % k != 0)
s = (lambda n, p, k:
    [i for i in range(1, n + 1)
        if p(i, n, k)])
A = s(n, p, k)
print(len(A)) # 42, I wonder why? :-P

Description:

• n: Our number
• p: Predicate, which is that it is a divisor and not divisible by 6
• s: Sequence generator, given n and a predicate
• A: The set of integer divisors verifying the predicate