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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 composite numbers are exactly the numbers that are not prime and not a ...
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 ...
This is a list of articles about prime numbers. A prime number (or prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. By Euclid's theorem, there are an infinite number of prime numbers. Subsets of the prime numbers may be generated with various formulas for primes.
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, 1 × 5 or 5 × 1, involve 5 itself. However, 4 is composite because it is a ...
A Gaussian integer is either the zero, one of the four units (±1, ± i ), a Gaussian prime or composite. The article is a table of Gaussian Integers x + iy followed either by an explicit factorization or followed by the label (p) if the integer is a Gaussian prime. The factorizations take the form of an optional unit multiplied by integer ...
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.