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58 lines
1.2 KiB
Python
58 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 triangle_number_generator():
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for n in range(1, 1000000):
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yield n * (n + 1) // 2
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def count_divisors(n):
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divisors_count = 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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divisors_count *= multiplicity + 1
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i += 1
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if n > 1:
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divisors_count *= 2
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return divisors_count
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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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return next(i for i in triangle_number_generator() if count_divisors(i) > 500)
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if __name__ == "__main__":
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print(solution())
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