Integer Integer An integer (from the Latin "integer" meaning "whole") is a number that can be written without a fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, , and are not. The set of integers consists of zero (), the positive natural numbers (, , , …), also called "whole numbers" or "counting numbers", and their additive inverses (the negative integers, i.e., −1, −2, −3, …). The set of integers is often denoted by a boldface Z ("") or blackboard bold formula_1 (Unicode U+2124 ℤ) standing for the German word "Zahlen" (, "numbers"). The integers form
Arithmetic number asymptotically where "c" = 2 + o(1). A number "N" is arithmetic if the number of divisors "d"("N") divides the sum of divisors σ("N"). It is known that the density of integers "N" obeying the stronger condition that "d"("N") divides σ("N") is 1/2. Arithmetic number In number theory, an arithmetic number is an integer for which the average of its positive divisors is also an integer. For instance, 6 is an arithmetic number because the average of its divisors is which is also an integer. However, 2 is not an arithmetic number because its only divisors are 1 and 2,