![cover image](https://wikiwandv2-19431.kxcdn.com/_next/image?url=https://upload.wikimedia.org/wikipedia/commons/thumb/2/20/Divisor.svg/640px-Divisor.svg.png&w=640&q=50)
Divisor function
Arithmetic function related to the divisors of an integer / From Wikipedia, the free encyclopedia
"Robin's theorem" redirects here. For Robbins' theorem in graph theory, see Robbins' theorem.
In mathematics, and specifically in number theory, a divisor function is an arithmetic function related to the divisors of an integer. When referred to as the divisor function, it counts the number of divisors of an integer (including 1 and the number itself). It appears in a number of remarkable identities, including relationships on the Riemann zeta function and the Eisenstein series of modular forms. Divisor functions were studied by Ramanujan, who gave a number of important congruences and identities; these are treated separately in the article Ramanujan's sum.
![Thumb image](http://upload.wikimedia.org/wikipedia/commons/thumb/2/20/Divisor.svg/320px-Divisor.svg.png)
![Thumb image](http://upload.wikimedia.org/wikipedia/commons/thumb/a/ab/Sigma_function.svg/320px-Sigma_function.svg.png)
![Thumb image](http://upload.wikimedia.org/wikipedia/commons/thumb/3/3c/Divisor_square.svg/320px-Divisor_square.svg.png)
![Thumb image](http://upload.wikimedia.org/wikipedia/commons/thumb/d/de/Divisor_cube.svg/320px-Divisor_cube.svg.png)
A related function is the divisor summatory function, which, as the name implies, is a sum over the divisor function.