Highly composite number

Numbers with many divisors

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. A related concept is that of a largely composite number, a positive integer that has at least as many divisors as all smaller positive integers.

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