Integer sequences

Highly composite number

A highly composite number is a positive integer with more divisors than any smaller positive integer has. The related concept of largely composite number refers to a positive integer which has at least as many divisors as any smaller positive integer. The name can be somewhat misleading, as two highly composite numbers (1 and 2) are not actually composite numbers; however, all further terms are. The late mathematician Jean-Pierre Kahane has suggested that Plato must have known about highly composite numbers as he deliberately chose 5040 as the ideal number of citizens in a city as 5040 has more divisors than any numbers less than it. Ramanujan wrote and titled his paper on the subject in 1915. (Wikipedia).

Highly composite number
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Related pages

Highly totient number | Composite number | Superior highly composite number | Table of divisors | Euler's totient function | Prime signature | Integer | Fundamental theorem of arithmetic | Numberphile | Paul Erdős | Round number | Divisor | Abundant number | Harshad number | Primorial | Smooth number | Practical number