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* ci(pre-commit): Add pep8-naming to `pre-commit` hooks (#7038) * refactor: Fix naming conventions (#7038) * Update arithmetic_analysis/lu_decomposition.py Co-authored-by: Christian Clauss <cclauss@me.com> * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * refactor(lu_decomposition): Replace `NDArray` with `ArrayLike` (#7038) * chore: Fix naming conventions in doctests (#7038) * fix: Temporarily disable project euler problem 104 (#7069) * chore: Fix naming conventions in doctests (#7038) Co-authored-by: Christian Clauss <cclauss@me.com> Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
63 lines
1.2 KiB
Python
63 lines
1.2 KiB
Python
"""
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Highly divisible triangular numbers
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Problem 12
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The sequence of triangle numbers is generated by adding the natural numbers. So
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the 7th triangle number would be 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28. The first ten
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terms would be:
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1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...
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Let us list the factors of the first seven triangle numbers:
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1: 1
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3: 1,3
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6: 1,2,3,6
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10: 1,2,5,10
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15: 1,3,5,15
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21: 1,3,7,21
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28: 1,2,4,7,14,28
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We can see that 28 is the first triangle number to have over five divisors.
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What is the value of the first triangle number to have over five hundred
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divisors?
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"""
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def count_divisors(n):
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n_divisors = 1
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i = 2
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while i * i <= n:
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multiplicity = 0
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while n % i == 0:
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n //= i
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multiplicity += 1
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n_divisors *= multiplicity + 1
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i += 1
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if n > 1:
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n_divisors *= 2
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return n_divisors
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def solution():
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"""Returns the value of the first triangle number to have over five hundred
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divisors.
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>>> solution()
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76576500
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"""
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t_num = 1
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i = 1
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while True:
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i += 1
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t_num += i
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if count_divisors(t_num) > 500:
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break
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return t_num
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if __name__ == "__main__":
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print(solution())
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