# On Deficient Perfect Numbers with Four Distinct Prime Factors

## TL;DR

This paper investigates odd deficient perfect numbers with four distinct prime factors, providing new results on their properties and existence.

## Contribution

It presents new theoretical results concerning the structure and properties of odd deficient perfect numbers with four prime factors.

## Key findings

- Identifies conditions under which such numbers can exist.
- Provides constraints on the prime factorization of these numbers.
- Advances understanding of deficient perfect numbers in number theory.

## Abstract

For a positive integer $n$, if $\sigma(n)$ denotes the sum of the positive divisors of $n$, then $n$ is called a deficient perfect number if $\sigma(n)=2n-d$ for some positive divisor $d$ of $n$. In this paper, we prove some results about odd deficient perfect numbers with four distinct prime factors.