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, and their average 3/2 is not an integer.

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 )2 divides σ(N ) is 1/2.