This code defines three functions: prime_factors to calculate the unique prime factors of a number, overlap to remove duplicate elements from two lists, and uses these functions to calculate the product of unique prime factors of numbers from 1 to 20. The functions are then exported as part of the module, making them available for import by other modules.

Run example

npm run import -- "rosetta euler python 005"

rosetta euler python 005

from operator import mul
from functools import reduce

def prime_factors(n):
    found = False
    if isinstance(n, str):
        try:
            n = int(n)
        except ValueError:
            try:
                n = float(n)
            except ValueError:
              raise

    v = 2

    i = 2

    while i < n -1 and found == False:
        if n % i == 0:
            found = True

            v = i

        i += 1

    if found:
        factors = [v] + prime_factors(n // v)
    else:
        factors = [n]

    return factors

def overlap(a, b):
    for n in b:
        if n in a:
            a.remove(n)

    result = sorted(a + b)


    return result

#print(reduce(mul, reduce(overlap, [prime_factors(x) for x in range(1, 21)])))
__all__ = {
  "prime_factors": prime_factors,
  "overlap": overlap
}

python
# Import the required modules
import math

def prime_factors(n):
    """
    Returns a list of prime factors of a given number.

    Args:
    n (int or str): The number to find prime factors for. Can be a string representation of an integer.

    Returns:
    list: A list of prime factors.

    Raises:
    ValueError: If the input is not a valid integer or float.
    """

    # Try to convert the input to an integer or float
    try:
        n = int(n)
    except ValueError:
        try:
            n = float(n)
            n = int(n)  # Ensure n is an integer
        except ValueError:
            raise ValueError("Input must be a valid integer or float")

    # Initialize the first prime number and the list of factors
    v = 2
    factors = []

    # Only check divisibility up to the square root of n
    for i in range(2, math.isqrt(n) + 1):
        # Check if n is divisible by i
        while n % i == 0:
            # If it is, add i to the list of factors and divide n by i
            factors.append(i)
            n = n // i

    # If n is a prime number greater than 2, add it to the list of factors
    if n > 2:
        factors.append(n)

    return factors

def overlap(a, b):
    """
    Returns a sorted list of elements present in both a and b, with duplicates removed.

    Args:
    a (list): The first list.
    b (list): The second list.

    Returns:
    list: A sorted list of unique elements present in both a and b.
    """

    # Initialize the result as an empty list
    result = []

    # Iterate over the elements in a and b
    for n in a + b:
        # If the element is not already in the result, add it
        if n not in result:
            result.append(n)

    # Sort the result
    result.sort()

    return result

# Define a function to calculate the product of a list of numbers
def product(numbers):
    """
    Returns the product of a list of numbers.

    Args:
    numbers (list): A list of numbers.

    Returns:
    int: The product of the numbers in the list.
    """

    # Use the reduce function from the math module to calculate the product
    return math.prod(numbers)

def main():
    # Calculate the product of the prime factors of numbers from 1 to 20
    result = product(reduce(overlap, (prime_factors(x) for x in range(1, 21))))

    # Print the result
    print(result)

if __name__ == "__main__":
    main()

Code Breakdown

Importing Modules

from operator import mul
from functools import reduce

The code imports the mul function from the operator module, which is used for element-wise multiplication, and the reduce function from the functools module, which is used to apply a function cumulatively to the elements of a sequence.

prime_factors Function

def prime_factors(n):
   ...

This function calculates the prime factors of a given number n. It does the following:

1. Checks if n is a string, and if so, attempts to convert it to an integer or float. If this fails, it raises an exception.
2. Initializes two variables: v to 2 (the first prime number) and found to False.
3. Enters a while loop that continues until i is greater than or equal to n or found is True.
4. Inside the loop, it checks if n is divisible by i. If it is, it sets found to True and assigns the value of i to v.
5. If found is True, it recursively calls the prime_factors function with n divided by v and adds the result to a list containing v. Otherwise, it returns a list containing n.

overlap Function

def overlap(a, b):
   ...

This function removes elements of list b from list a and returns the resulting merged list in sorted order.

1. It iterates over the elements of b and removes any elements found in b from a.
2. It merges the resulting lists a and b and sorts the result.

Example Usage

print(reduce(mul, reduce(overlap, [prime_factors(x) for x in range(1, 21)])))

This line of code calculates the product of the unique prime factors of the numbers from 1 to 20.

Module Exports

__all__ = {
  "prime_factors": prime_factors,
  "overlap": overlap
}

This line exports the prime_factors and overlap functions as part of the current module, making them available for import by other modules.