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We call $n$ a highly composite number if $d(n)>d(m)$ for all $m<n$ where $d(n)$ is the number of divisors of $n$ The first several are 1, 2, 4, 6, 12, 24. The sequence is A002182 in Sloane's OEIS.
The integer $n$ is superior highly composite if there is an $\epsilon>0$ such that for all $m\not=n$ $$d(n) n^{-\epsilon} > d(m) m^{-\epsilon}.$$ The first several superior highly composite numbers are 2, 6, 12, 60, 120, 360. The sequence is A002201 in Sloane's encyclopedia.
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- L. Alaoglu and P. Erdös, On highly composite and similar numbers. Trans. Amer. Math. Soc. 56 (1944), 448-469. Available at www.jstor.org
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