projecteuler.py

import math

##### Helper functions #####
def is_divisible(number, values):
    """Returns True if number is evenly divisible by all values in [values]."""
    for i in values:
        if number % i != 0:
            return False
    return True

def is_prime(number):
    """Returns True if number is prime."""
    p = 2
    sqrt = math.sqrt(number)
    while p <= sqrt:
        if number % p == 0:
            return False
        if p > 2:
            p += 2
        else:
            p += 1
    return True

def find_divisors(number):
    """Returns a list of factors of number."""
    div_pairs = [[i, number//i] for i in range(1, int(number**0.5)+1) if number % i == 0]
    return reduce(list.__add__, div_pairs)

def proper_divisors(number):
    """Returns a set of proper divisors of a number (excluding the number itself)."""
    if number == 1:
        div = [1]
        return set(div)
    div_pairs = [[i, number//i] for i in range(1, int(number**0.5)+1) if number % i == 0]
    div = reduce(list.__add__, div_pairs)
    div.remove(number)
    return set(div)

def is_coprime(n1, n2):
    """Returns True if n1 is coprime to n2, i.e. their largest common factor is 1."""
    return set(find_divisors(n1)).intersection(set(find_divisors(n2))) == set([1])
##### Helper functions #####