Divisor function: Difference between revisions

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[[Image:Divisor square.svg|thumb|right|Sum of the squares of divisors, ''σ''₂(''n''), up to ''n'' = 250]]

[[Image:Divisor cube.svg|thumb|right|Sum of cubes of divisors, ''σ''₃(''n'') up to ''n'' = 250]]

jgkjSvkcsvhdvcjkvbc;vhihvoscho'fhoifhvohbhcibhfpbfopbInIn [[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.