  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.
