Sidney Zhang
13d5d27c5a
📝 feat(0021.AmicableNumbers/readme.md)：添加亲和数对文档的中文翻译 ✨ feat(0022)：新增欧拉问题22解决方案，包含姓名文件和处理脚本 ✨ feat(0023)：新增欧拉问题23解决方案，包含三种实现和文档说明 📝 docs(solutions/0067.MaxPathSum2)：新增热带半环理论综述文档 新增关于热带半环（Tropical Semiring）的详细综述文档，涵盖其数学原理、与代数几何的联系（热带几何）、在量子力学与量子信息中的应用，以及其他跨学科应用领域。文档系统性地介绍了热带半环的基本理论结构，包括min-plus/max-plus代数、幂等性与分配律，以及其与全序集和格论的联系。同时深入探讨了热带几何的核心概念（如热带化、热带簇、Amoebas和Newton多边形）及其在代数几何中的应用（如热带Bézout定理、拓扑不变量计算和枚举几何）。文档还综述了热带半环在量子力学（如热带量子理论、非厄米系统特殊点分析）和量子信息（如贝尔不等式分析、热带张量网络）中的前沿应用，并展望了其在密码学、生物信息学等领域的潜力。该文档旨在为相关领域的研究者提供一个全面的理论参考。
71 lines
2.1 KiB
Python
71 lines
2.1 KiB
Python
"""
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A perfect number is a number for which the sum of its proper divisors is exactly equal to the number.
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For example, the sum of the proper divisors of 28 would be 1 + 2 + 4 + 7 + 14 = 28,
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which means that 28 is a perfect number.
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A number n is called deficient if the sum of its proper divisors is less than n and
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it is called abundant if this sum exceeds n .
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As 12 is the smallest abundant number, 1+2+3+4+6 = 16,
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the smallest number that can be written as the sum of two abundant numbers is 24.
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By mathematical analysis, it can be shown that all integers greater than 28123 can be written
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as the sum of two abundant numbers.
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However, this upper limit cannot be reduced any further by analysis even though
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it is known that the greatest number that cannot be expressed as the sum of two abundant numbers is less than
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this limit.
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Find the sum of all the positive integers which cannot be written as the sum of two abundant numbers.
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"""
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import time
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def timer(func):
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def wrapper(*args, **kwargs):
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start_time = time.time()
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result = func(*args, **kwargs)
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end_time = time.time()
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print(f"Execution time: {end_time - start_time} seconds")
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return result
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return wrapper
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def is_abundant(n: int) -> bool:
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if n % 12 == 0:
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return True
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sum_divisors = [1]
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for i in range(2, n):
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if n % i == 0:
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if i not in sum_divisors:
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sum_divisors.append(i)
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if n // i not in sum_divisors:
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sum_divisors.append(n // i)
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if sum(sum_divisors) > n:
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return True
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return sum(sum_divisors) > n
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def is_sum_of_two_abundants(n: int) -> bool:
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if n < 24:
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return False
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if n == 24:
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return True
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for i in range(12, n // 2 + 1):
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if is_abundant(i) and is_abundant(n - i):
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return True
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return False
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@timer
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def main():
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limit = 28123
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non_abundant_sums = [
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i for i in range(1, limit + 1) if not is_sum_of_two_abundants(i)
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]
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print(sum(non_abundant_sums))
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if __name__ == "__main__":
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main()
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