关于Zumkeller与$K$ -分层数的区别
On the differences between Zumkeller and $K$-layered numbers
摘要：
一个正整数$n$称为Zumkeller数，如果$n$的正因子可以被划分为两个不相交的子集，其和\cite{zumkeller}相等。本文在第一节中研究了Zumkeller数之间的区别，证明了一个比Green-Tao定理更强的Zumkeller数定理。在第二节中，我们定义了$k$ -分层数，它是Zumkeller数的推广，并研究了$k$ -分层数之间的区别。我们还证明了一个比Green-Tao定理更强的4层数定理。
英文摘要：
A positive integer $n$ is said to be a Zumkeller number if the positive divisors of $n$ can be partitioned into two disjoint subsets of equal sum \cite{zumkeller}. In this paper, in the first section, we investigate differences between Zumkeller numbers and prove a theorem stronger than Green-Tao theorem for Zumkeller numbers. In the second section, we define $k$-layered numbers which are the generalization of Zumkeller numbers and investigate differences between $k$-layered numbers. We also prove a theorem stronger than Green-Tao theorem for 4-layered numbers.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
