mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-11-24 13:31:07 +00:00
cecf43d648
* Pyupgrade to Python 3.9
* updating DIRECTORY.md
Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
48 lines
1.1 KiB
Python
48 lines
1.1 KiB
Python
"""
|
|
Highly divisible triangular numbers
|
|
Problem 12
|
|
The sequence of triangle numbers is generated by adding the natural numbers. So
|
|
the 7th triangle number would be 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28. The first ten
|
|
terms would be:
|
|
|
|
1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...
|
|
|
|
Let us list the factors of the first seven triangle numbers:
|
|
|
|
1: 1
|
|
3: 1,3
|
|
6: 1,2,3,6
|
|
10: 1,2,5,10
|
|
15: 1,3,5,15
|
|
21: 1,3,7,21
|
|
28: 1,2,4,7,14,28
|
|
We can see that 28 is the first triangle number to have over five divisors.
|
|
|
|
What is the value of the first triangle number to have over five hundred
|
|
divisors?
|
|
"""
|
|
|
|
|
|
def triangle_number_generator():
|
|
for n in range(1, 1000000):
|
|
yield n * (n + 1) // 2
|
|
|
|
|
|
def count_divisors(n):
|
|
return sum(2 for i in range(1, int(n ** 0.5) + 1) if n % i == 0 and i * i != n)
|
|
|
|
|
|
def solution():
|
|
"""Returns the value of the first triangle number to have over five hundred
|
|
divisors.
|
|
|
|
# The code below has been commented due to slow execution affecting Travis.
|
|
# >>> solution()
|
|
# 76576500
|
|
"""
|
|
return next(i for i in triangle_number_generator() if count_divisors(i) > 500)
|
|
|
|
|
|
if __name__ == "__main__":
|
|
print(solution())
|