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Composite numbers can be arranged into rectangles but prime numbers cannot. A composite number is a positive integer that can be formed by multiplying two smaller positive integers. Equivalently, it is a positive integer that has at least one divisor other than 1 and itself. [1] [2] Every positive integer is composite, prime, or the unit 1, so ...
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 ...
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.
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 ...
Carmichael number. In number theory, a Carmichael number is a composite number which in modular arithmetic satisfies the congruence relation : for all integers . [1] The relation may also be expressed [2] in the form: for all integers that are relatively prime to . They are infinite in number.
Every positive integer greater than 1 is either the product of two or more integer factors greater than 1, in which case it is called a composite number, or it is not, in which case it is called a prime number. For example, 15 is a composite number because 15 = 3 · 5, but 7 is a prime number because it cannot be decomposed in this way. If one ...
Every integer greater than one is either prime or composite. Polygonal numbers: These are numbers that can be represented as dots that are arranged in the shape of a regular polygon, including Triangular numbers, Square numbers, Pentagonal numbers, Hexagonal numbers, Heptagonal numbers, Octagonal numbers, Nonagonal numbers, Decagonal numbers ...
In number theory, a Smith number is a composite number for which, in a given number base, the sum of its digits is equal to the sum of the digits in its prime factorization in the same base. In the case of numbers that are not square-free , the factorization is written without exponents, writing the repeated factor as many times as needed.
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