37 lines
1.1 KiB
Python
37 lines
1.1 KiB
Python
#!/usr/bin/env python3
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# Let d(n) be defined as the sum of proper divisors of n (numbers less than n which divide evenly into n).
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# If d(a) = b and d(b) = a, where a ≠ b, then a and b are an amicable pair and each of a and b are called amicable numbers.
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#
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# For example, the proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110; therefore d(220) = 284.
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# The proper divisors of 284 are 1, 2, 4, 71 and 142; so d(284) = 220.
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#
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# Evaluate the sum of all the amicable numbers under 10000.
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from projecteuler import sum_of_divisors, timing
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@timing
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def p021() -> None:
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_sum = 0
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for i in range(2, 10000):
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# Calculate the sum of proper divisors with the function
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# implemented in projecteuler.py.
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n = sum_of_divisors(i)
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# If i!=n and the sum of proper divisors of n=i,
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# sum the pair of numbers and add it to the total.
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if i != n and sum_of_divisors(n) == i:
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_sum = _sum + i + n
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_sum = _sum // 2
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print('Project Euler, Problem 21')
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print(f'Answer: {_sum}')
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if __name__ == '__main__':
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p021()
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