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20 (twenty) is the natural number following 19 and preceding 21.
A highly composite number is a positive integer that has more divisors than all smaller positive integers. A related concept is that of a largely composite number, a positive integer that has at least as many divisors as all smaller positive integers. The name can be somewhat misleading, as the first two highly composite numbers are not actually composite numbers; however, all further terms are.
In number theory, a Wilson prime is a prime number such that divides , where "" denotes the factorial function; compare this with Wilson's theorem, which states that every prime divides . Both are named for 18th-century English mathematician John Wilson; in 1770, Edward Waring credited the theorem to Wilson, although it had been stated centuries earlier by Ibn al-Haytham.
In mathematics, a P-multimagic square is a magic square that remains magic even if all its numbers are replaced by their kth powers for 1 ≤ k ≤ P. 2-multimagic squares are called bimagic, 3-multimagic squares are called trimagic, 4-multimagic squares tetramagic, and 5-multimagic squares pentamagic.
105 is the natural number following 104 and preceding 106.
In mathematics, a primorial prime is a prime number of the form pn# ± 1, where pn# is the primorial of pn.
In mathematics, and more particularly in number theory, primorial, denoted by "pn#", is a function from natural numbers to natural numbers similar to the factorial function, but rather than successively multiplying positive integers, the function only multiplies prime numbers.
In mathematics, and more specifically number theory, the hyperfactorial of a positive integer is the product of the numbers of the form from to .
In mathematics, and more specifically number theory, the superfactorial of a positive integer is the product of the first factorials. They are a special case of the Jordan–Pólya numbers, which are products of arbitrary collections of factorials.
In number theory, a Wagstaff prime is a prime number of the form
Lucas pseudoprimes and Fibonacci pseudoprimes are composite integers that pass certain tests which all primes and very few composite numbers pass: in this case, criteria relative to some Lucas sequence.
100,000 (one hundred thousand) is the natural number following 99,999 and preceding 100,001. In scientific notation, it is written as 105.
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.
In mathematics, an alternating factorial is the absolute value of the alternating sum of the first n factorials of positive integers.
In number theory, friendly numbers are two or more natural numbers with a common abundancy index, the ratio between the sum of divisors of a number and the number itself. Two numbers with the same "abundancy" form a friendly pair; n numbers with the same abundancy form a friendly n-tuple.
In mathematics, the cake number, denoted by Cn, is the maximum of the number of regions into which a 3-dimensional cube can be partitioned by exactly n planes. The cake number is so-called because one may imagine each partition of the cube by a plane as a slice made by a knife through a cube-shaped cake. It is the 3D analogue of the lazy caterer's sequence.
A Fortunate number, named after Reo Fortune, is the smallest integer m > 1 such that, for a given positive integer n, pn# + m is a prime number, where the primorial pn# is the product of the first n prime numbers.
30,000 is the natural number that comes after 29,999 and before 30,001.
In mathematics, the Fibonorialn!F, also called the Fibonacci factorial, where n is a nonnegative integer, is defined as the product of the first n positive Fibonacci numbers, i.e.
Multiplicative partitions of factorials are expressions of values of the factorial function as products of powers of prime numbers. They have been studied by Paul Erdős and others.