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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. Yet another way to classify composite numbers ...
The first 41 highly composite numbers are listed in the table below (sequence A002182 in the OEIS). The number of divisors is given in the column labeled d ( n ). Asterisks indicate superior highly composite numbers .
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.
The tables contain the prime factorization of the natural numbers from 1 to 1000. When n is a prime number, the prime factorization is just n itself, written in bold below. The number 1 is called a unit. It has no prime factors and is neither prime nor composite.
In number theory, a superior highly composite number is a natural number which, in a particular rigorous sense, has many divisors. ... Toggle the table of contents.
Toggle the table of contents. List of types of numbers. 8 languages. ... Every integer greater than one is either prime or composite. Polygonal numbers: ...
Toggle the table of contents. List of integer sequences. 3 languages. ... Composite numbers n such that a n − 1 ≡ 1 (mod n) if a is coprime with n. A002997 ...
For composite n < 200, the following is a table of all bases b < n which n is a Fermat pseudoprime. If a composite number n is not in the table (or n is in the sequence A209211), then n is a pseudoprime only to the trivial base 1 modulo n.