# Analytical Representations of Divisors of Integers

## TL;DR

This paper explores analytical expressions that represent divisors of natural numbers, revealing connections to the sieve of Eratosthenes, with a focus on pedagogical presentation and some novel formulas.

## Contribution

It introduces new formulas and insights into how analytical expressions can encode divisor information and relate to classical algorithms like the sieve of Eratosthenes.

## Key findings

- Expressions encode sieve of Eratosthenes
- Some formulas are new
- Pedagogical presentation

## Abstract

Certain analytical expressions which "feel" the divisors of natural numbers are investigated. We show that these expressions encode to some extent the well-known algorithm of the sieve of Eratosthenes. Most part of the text is written in pedagogical style, however some formulas are new.