Editing Divisor function (section)

{{redirect|Robin's theorem|Robbins' theorem in graph theory|Robbins' theorem}}
{{short description|Arithmetic function related to the divisors of an integer}}

[[Image:Divisor.svg|thumb|right|Divisor function ''σ''<sub>0</sub>(''n'') up to ''n''&nbsp;=&nbsp;250]]
[[Image:Sigma function.svg|thumb|right|Sigma function ''σ''<sub>1</sub>(''n'') up to ''n''&nbsp;=&nbsp;250]]
[[Image:Divisor square.svg|thumb|right|Sum of the squares of divisors, ''σ''<sub>2</sub>(''n''), up to ''n''&nbsp;=&nbsp;250]]
[[Image:Divisor cube.svg|thumb|right|Sum of cubes of divisors, ''σ''<sub>3</sub>(''n'') up to ''n''&nbsp;=&nbsp;250]]
In [[mathematics]], and specifically in [[number theory]], a '''divisor function''' is an [[arithmetic function]] related to the [[divisor]]s 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 form]]s. Divisor functions were studied by [[Ramanujan]], who gave a number of important [[Modular arithmetic|congruences]] and [[identity (mathematics)|identities]]; these are treated separately in the article [[Ramanujan's sum]].

A related function is the [[divisor summatory function]], which, as the name implies, is a sum over the divisor function.