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Transcript 
highly composite number∗
Kevin OBryant†
2013-03-21 16:06:12
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 > 0 such that for
all m 6= n,
d(n)n− > d(m)m− .
The first several superior highly composite numbers are 2, 6, 12, 60, 120, 360.
The sequence is A002201 in Sloane’s encyclopedia.
References
[1] L. Alaoglu and P. Erdös, On highly composite and similar numbers. Trans.
Amer. Math. Soc. 56 (1944), 448–469. Available at www.jstor.org
∗ hHighlyCompositeNumberi created: h2013-03-21i by: hKevin OBryanti version: h34347i
Privacy setting: h1i hDefinitioni h11N56i
† This text is available under the Creative Commons Attribution/Share-Alike License 3.0.
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