43 lines
1.1 KiB
Python
43 lines
1.1 KiB
Python
# Highly divisible triangular number
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# Problem 12
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# 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:
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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 divisors?
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from collections import Counter
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from functools import reduce
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import util
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target = 76576500
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for i in range(1, 100000):
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result = reduce(lambda x,y: x + y, list(range(1, i + 1)))
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# divisers = find_divisers(result)
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factors = util.find_prime_factors(result)
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total_count = 1
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for factor, count in Counter(factors).items():
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total_count *= count + 1
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if (total_count >= 500):
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# print(i)
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# print(total_count)
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print(result)
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print(result == target)
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break
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