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Highly composite numbers greater than 6 are also abundant numbers. One need only look at the three largest proper divisors of a particular highly composite number to ascertain this fact. It is false that all highly composite numbers are also Harshad numbers in base 10. The first highly composite number that is not a Harshad number is ...
The first 15 superior highly composite numbers, 2, 6, 12, 60, 120, 360, 2520, 5040, 55440, 720720, 1441440, 4324320, 21621600, 367567200, 6983776800 (sequence A002201 in the OEIS) are also the first 15 colossally abundant numbers, which meet a similar condition based on the sum-of-divisors function rather than the number of divisors. Neither ...
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 list of articles about numbers (not about numerals). Topics include powers of ten, notable integers, prime and cardinal numbers, and the myriad system.
5040 (five thousand [and] forty) is the natural number following 5039 and preceding 5041.. It is a factorial (7!), the 8th superior highly composite number, [1] the 19th highly composite number, [2] an abundant number, the 8th colossally abundant number [3] and the number of permutations of 4 items out of 10 choices (10 × 9 × 8 × 7 = 5040).
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.
360 is divisible by the number of its divisors , and it is the smallest number divisible by every natural number from 1 to 10, except 7. Furthermore, one of the divisors of 360 is 72, which is the number of primes below it. 360 is the sum of twin primes (179 + 181) and the sum of four consecutive powers of three (9 + 27 + 81 + 243).
Base systems corresponding to primorials (such as base 30, not to be confused with the primorial number system) have a lower proportion of repeating fractions than any smaller base. Every primorial is a sparsely totient number. [10] The n-compositorial of a composite number n is the product of all composite numbers up to and including n. [11]