论文标题
在丰度的边界上搜索奇怪的数字
Searching on the boundary of abundance for odd weird numbers
论文作者
论文摘要
怪异的数字是不伪造的大量数字。自从引入以来，奇怪数字的存在一直是一个空旷的问题。在这项工作中，我们描述了搜索奇怪数字的计算工作，这表明它们的不存在高达$ 10^{21} $。我们还搜索了高达$ 10^{28} $的数字，其丰度低于$ 10^{14} $，无济于事。我们加快搜索的方法可以看作是在组合优化领域中反向搜索的应用，并且对于对具有至关重要的特殊属性的自然数量的其他类似追求可能很有用，这些属性依赖于它们的分解。
Weird numbers are abundant numbers that are not pseudoperfect. Since their introduction, the existence of odd weird numbers has been an open problem. In this work, we describe our computational effort to search for odd weird numbers, which shows their non-existence up to $10^{21}$. We also searched up to $10^{28}$ for numbers with an abundance below $10^{14}$, to no avail. Our approach to speed up the search can be viewed as an application of reverse search in the domain of combinatorial optimization, and may be useful for other similar quest for natural numbers with special properties that depend crucially on their factorization.
