An integer n > 1 for which some epsilon > 0 makes d(n)/n^epsilon maximal among all integers greater than 1, where d counts positive divisors.
The first few superior highly composite numbers are: 2, 6, 12, 60, 120, 360, 2520, 5040, 55440, 720720, …
10 of the first one million positive integers are superior highly composite.
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