论文标题
Zumkeller号码和$ K $ aylered号码的某些属性
Some properties of Zumkeller numbers and $k$-layered numbers
论文作者
论文摘要
概括一个完美数字的概念是Zumkeller或Integer Perfect数字，由Zumkeller在2003年推出。如果可以将其除法分配为具有相同总和的两个集合，那么正整数$ n $是Zumkeller号码，这将是$σ（n）/2 $。进一步概括，如果可以将其除数分配为$ k $ sets，则我们将$ n $ n $ a $ a $ a $ a $ aylered数字均等。 在本文中，我们完全表征了Zumkeller的数字，其中有两个不同的主要因素，并在Zumkeller数字中具有两个以上不同的主要因素的质量分解范围。我们还表征了$ k $的数字，其中有两个不同的主要因素，甚至有两个以上奇数质量因素。还讨论了有关这些数字及其与实际数字和谐波均值数字的关系的其他结果。
Generalizing the concept of a perfect number is a Zumkeller or integer perfect number that was introduced by Zumkeller in 2003. The positive integer $n$ is a Zumkeller number if its divisors can be partitioned into two sets with the same sum, which will be $σ(n)/2$. Generalizing even further, we call $n$ a $k$-layered number if its divisors can be partitioned into $k$ sets with equal sum. In this paper, we completely characterize Zumkeller numbers with two distinct prime factors and give some bounds for prime factorization in case of Zumkeller numbers with more than two distinct prime factors. We also characterize $k$-layered numbers with two distinct prime factors and even $k$-layered numbers with more than two distinct odd prime factors. Some other results concerning these numbers and their relationship with practical numbers and Harmonic mean numbers are also discussed.
