A positive integer n is called a highly composite number if it has more
divisors than any predecessor.
Let d(n) be the number of divisors of n, then
n is highly composite if
d(m) < d(n) for all positive m < n.
For example, n = 120 is highly composite because it has 16 divisors (so d(120) = 16)
and all smaller integers have fewer than 16 divisors.