Back دالة القواسم Arabic Сигма-функция (теория на числата) Bulgarian গুণনীয়ক ফাংশন Bengali/Bangla Teilerfunktion German Divizora funkcio Esperanto Función divisor Spanish Zatitzaile funtzio Basque Sigmafunktio Finnish Fonction somme des puissances k-ièmes des diviseurs French Función divisor Galician
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.
A related function is the divisor summatory function, which, as the name implies, is a sum over the divisor function.