Multidivisors

Multidivisors is a mathematical concept that refers to numbers that possess a specific property related to their divisors. A number n is considered a multidivisor if the number of divisors of n is itself a divisor of n. For example, consider the number 12. Its divisors are 1, 2, 3, 4, 6, and 12. The count of these divisors is 6. Since 6 is a divisor of 12, the number 12 is a multidivisor.

The sequence of multidivisors begins with 1, 12, 18, 24, 36, 48, 60, 72, 84, 90, 96, 108, 120, 132, 144, 156, 168, 180, 192, 198, 204, 216, 228, 234, 240, 252, 264, 270, 276, 288, 300, and so on. These numbers are also known as highly composite numbers in a less strict sense, though the term highly composite number typically refers to numbers with more divisors than any smaller positive integer. The study of multidivisors is related to number theory and the properties of the divisor function, often denoted by sigma_0(n) or d(n), which counts the number of positive divisors of an integer n. An integer n is a multidivisor if d(n) divides n.