Python/project_euler/problem_006/sol4.py

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"""
Problem 6: https://projecteuler.net/problem=6
The sum of the squares of the first ten natural numbers is,
1^2 + 2^2 + ... + 10^2 = 385
The square of the sum of the first ten natural numbers is,
(1 + 2 + ... + 10)^2 = 552 = 3025
Hence the difference between the sum of the squares of the first ten natural
numbers and the square of the sum is 3025 385 = 2640.
Find the difference between the sum of the squares of the first N natural
numbers and the square of the sum.
"""
def solution(n: int = 100) -> int:
"""Returns the difference between the sum of the squares of the first n
natural numbers and the square of the sum.
>>> solution(10)
2640
>>> solution(15)
13160
>>> solution(20)
41230
>>> solution(50)
1582700
>>> solution()
25164150
"""
sum_of_squares = n * (n + 1) * (2 * n + 1) / 6
square_of_sum = (n * (n + 1) / 2) ** 2
return int(square_of_sum - sum_of_squares)
if __name__ == "__main__":
import doctest
doctest.testmod()
print(solution(int(input("Enter a number: ").strip())))