In this article, we are going to analyze in detail Arithmetic number, a topic that has generated a great debate in contemporary society. Arithmetic number is a topic of great relevance, since it affects a wide spectrum of the population and has repercussions on various aspects of daily life. Throughout this article, we will explore different perspectives on Arithmetic number, with the aim of shedding light on its implications and generating deep reflection. From its origin to its possible solutions, including its short and long-term consequences, Arithmetic number is a topic that deserves to be addressed with seriousness and rigor, which is why it is vitally important to delve into its analysis.
Integer where the average of its positive divisors is also an integer
Demonstration, with Cuisenaire rods, of the arithmetic nature of the number 6
In number theory, an arithmetic number is an integer for which the average of its positivedivisors 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.
The first numbers in the sequence of arithmetic numbers are
It is known that the natural density of such numbers is 1:[1] indeed, the proportion of numbers less than X which are not arithmetic is asymptotically[2]
where c = 2√log 2 + o(1).
A number N is arithmetic if the number of divisorsd(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.[1][2]
