Highly abundant number

A highly abundant number is a positive integer that has a particularly high ratio of the sum of its divisors to the number itself. More formally, a highly abundant number \( n \) satisfies the condition that for any integer \( m < n \), the sum of the divisors function \( \sigma(m) \) (which returns the sum of all positive divisors of \( m \)) is less than \( \sigma(n) \) divided by \( n \).