A highly composite number is a positive integer that has more divisors than all smaller positive integers. If d(n) denotes the number of divisors of a positive integer n, then a positive integer N is highly composite if d(N) > d(n) for all n < N. For example, 6 is highly composite because d(6) = 4, and for n = 1,2,3,4,5, you get d(n) = 1,2,2,3,2, respectively, which are all less than 4.