代码拉取完成,页面将自动刷新
"""
A perfect number is a number for which the sum of its proper divisors is exactly
equal to the number. For example, the sum of the proper divisors of 28 would be
1 + 2 + 4 + 7 + 14 = 28, which means that 28 is a perfect number.
A number n is called deficient if the sum of its proper divisors is less than n
and it is called abundant if this sum exceeds n.
As 12 is the smallest abundant number, 1 + 2 + 3 + 4 + 6 = 16, the smallest
number that can be written as the sum of two abundant numbers is 24. By
mathematical analysis, it can be shown that all integers greater than 28123
can be written as the sum of two abundant numbers. However, this upper limit
cannot be reduced any further by analysis even though it is known that the
greatest number that cannot be expressed as the sum of two abundant numbers
is less than this limit.
Find the sum of all the positive integers which cannot be written as the sum
of two abundant numbers.
"""
def solution(limit=28123):
"""
Finds the sum of all the positive integers which cannot be written as
the sum of two abundant numbers
as described by the statement above.
>>> solution()
4179871
"""
sum_divs = [1] * (limit + 1)
for i in range(2, int(limit**0.5) + 1):
sum_divs[i * i] += i
for k in range(i + 1, limit // i + 1):
sum_divs[k * i] += k + i
abundants = set()
res = 0
for n in range(1, limit + 1):
if sum_divs[n] > n:
abundants.add(n)
if not any((n - a in abundants) for a in abundants):
res += n
return res
if __name__ == "__main__":
print(solution())
此处可能存在不合适展示的内容,页面不予展示。您可通过相关编辑功能自查并修改。
如您确认内容无涉及 不当用语 / 纯广告导流 / 暴力 / 低俗色情 / 侵权 / 盗版 / 虚假 / 无价值内容或违法国家有关法律法规的内容,可点击提交进行申诉,我们将尽快为您处理。