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p012.py
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p012.py
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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:
# 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?
import itertools, math
def compute():
triangle = 0
for i in itertools.count(1):
triangle += i # This is the ith triangle number, i.e. num = 1 + 2 + ... + i = i * (i + 1) / 2
if num_divisors(triangle) > 500:
return str(triangle)
# Returns the number of integers in the range [1, n] that divide n.
def num_divisors(n):
end = math.floor(math.sqrt(n))
result = sum(2
for i in range(1, end + 1)
if n % i == 0)
if end**2 == n:
result -= 1
return result
if __name__ == "__main__":
print(compute())