# Two-layered numbers

## TL;DR

This paper introduces the concept of two-layered and half-layered numbers, exploring their properties and relationships with practical and Zumkeller numbers, expanding the understanding of divisor partitioning in number theory.

## Contribution

The paper defines new classes of numbers—two-layered and half-layered—and investigates their properties and connections to existing number classes.

## Key findings

- Two-layered numbers have specific divisor partition properties.
- Half-layered numbers relate to proper divisors and partitioning.
- Connections between these new classes and practical and Zumkeller numbers are established.

## Abstract

In this paper, first, I introduce two-layered numbers. Two-layered numbers are positive integers that their positive divisors except 1 can be partitioned into two disjoint subsets. Similarly, I defined a half-layered number as a positive integer n that its proper positive divisors excluding $1$ can be partitioned into two disjoint subsets. I also investigate the properties of two-layered and half-layered numbers and their relation with practical numbers and Zumkeller numbers.