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78 lines
1.9 KiB
Python
78 lines
1.9 KiB
Python
"""What is the value of the first triangle number to have over five hundred divisors?
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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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"""
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from e003 import pfactor
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from p054.poker import unique_combinations
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def triangle(n):
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x = 0
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for i in range(n + 1):
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x = x + i
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return x
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def badfactor(n):
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f = []
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for i in range(n, 0, -1):
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if n % i == 0:
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f.append(i)
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return f
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def product(l):
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p = 1
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for n in l:
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p = p * n
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return p
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def factor(n):
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primes = pfactor(n)
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factors = [1, n]
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pow = {}
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for p in primes:
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if p not in pow.keys():
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pow[p] = 0
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pow[p] = pow[p] + 1
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factors.append(p**pow[p])
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for p in [f for f in factors if f > 1]:
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f = n / p
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if f not in factors:
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factors.append(n / p)
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combos = unique_combinations(factors, 2)
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for c in combos:
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f = product(c)
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if f < n and n % f == 0 and f not in factors:
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factors.append(f)
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if n not in factors:
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factors.append(n)
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return sorted(set(factors))
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def main():
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i = 1
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while True:
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i = i + 1
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t = triangle(i)
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f = factor(t)
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print 'Checking triangle', i, t, len(f)
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if len(f) > 500:
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break
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print 'Triangle number {0} has {1} factors ({2})'.format(t, len(f), f)
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if __name__ == '__main__':
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main()
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