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The sequence of highly composite numbers (sequence A002182 in the OEIS) is a subset of the sequence of smallest numbers k with exactly n divisors (sequence A005179 in the OEIS ). Highly composite numbers whose number of divisors is also a highly composite number are. 1, 2, 6, 12, 60, 360, 1260, 2520, 5040, 55440, 277200, 720720, 3603600 ...
In number theory, a superior highly composite number is a natural number which, in a particular rigorous sense, has many divisors. Particularly, it is defined by a ratio between the number of divisors an integer has and that integer raised to some positive power. For any possible exponent, whichever integer has the greatest ratio is a superior ...
A number n that has more divisors than any x < n is a highly composite number (though the first two such numbers are 1 and 2). Composite numbers have also been called "rectangular numbers", but that name can also refer to the pronic numbers , numbers that are the product of two consecutive integers.
In mathematics. 360 is a highly composite number [1] and one of only seven numbers such that no number less than twice as much has more divisors; the others are 1, 2, 6, 12, 60, and 2520 (sequence A072938 in the OEIS ). 360 is also a superior highly composite number, a colossally abundant number, a refactorable number, a 5- smooth number, and a ...
Then in particular any superabundant number is an even integer, and it is a multiple of the k-th primorial #. In fact, the last exponent a k is equal to 1 except when n is 4 or 36. Superabundant numbers are closely related to highly composite numbers. Not all superabundant numbers are highly composite numbers.
Table of divisors. Plot of the number of divisors of integers from 1 to 1000. Highly composite numbers are in bold and superior highly composite numbers are starred. In the SVG file, hover over a bar to see its statistics. The tables below list all of the divisors of the numbers 1 to 1000. A divisor of an integer n is an integer m, for which n ...
5040 (number) 5040 ( five thousand [and] forty) is the natural number following 5039 and preceding 5041. It is a factorial (7!), a superior highly composite number, abundant number, colossally abundant number and the number of permutations of 4 items out of 10 choices (10 × 9 × 8 × 7 = 5040). It is also one less than a square, making (7, 71 ...
In mathematics. [edit] 60 is a highly composite number. [ 1 ] Because it is the sum of its unitary divisors (excluding itself), it is a unitary perfect number, [ 2 ] and it is an abundant number with an abundance of 48. Being ten times a perfect number, it is a semiperfect number. 60 is a Twin-prime sum of the fifth pair of twin-primes, 29 + 31.