Category: Integers A Friedman number is an integer which, in a given base, is the result of an expression using all its own digits in combination with any of the four basic arithmetic operators (+, -, ×, ÷) and sometimes exponentiation. ... In mathematics, a natural number is either a positive integer (1, 2, 3, 4, ...) or a non-negative integer (0, 1, 2, 3, 4, ...). The former definition is generally used in number theory, while the latter is preferred in set theory and computer science. ... English language spread in the United States. ... Diagram showing the geographical locations of selected languages and dialects of the British Isles. ... A highly totient number k is an integer that has more solutions to the equation &#966;(x) = k, where &#966; is Eulers totient function, than any integer below it. ... A harmonic divisor number, or Ore number, is a number whose divisors, averaged in a harmonic mean, results in an integer. ... In recreational mathematics, a repunit is a number like 11, 111, or 1111 that contains only the digit 1. ... A Motzkin number for a given number n is the number of different ways of drawing non-intersecting chords on a circle between n points. ... In mathematics, a Fermat number, named after Pierre de Fermat who first studied them, is a positive integer of the form where n is a nonnegative integer. ... The Bell numbers, named in honor of Eric Temple Bell, are a sequence of integers arising in combinatorics that begins thus (sequence A000110 in OEIS): In general, Bn is the number of partitions of a set of size n. ... In mathematics, a Keith number or repfigit number is an integer that appears as a term in a linear recurrence relation with initial terms based off its own digits. ... In mathematics, the Fibonacci numbers form a sequence defined recursively by: That is, after two starting values, each number is the sum of the two preceding numbers. ... A Wedderburn-Etherington number counts how many weakly binary trees can be constructed such that each graph vertex (not counting the root vertex) is adjacent to no more than three other such vertices, for a given number of nodes. ... In mathematics, a Mersenne number is a number that is one less than a power of two. ... In mathematics, a power of two is any of the nonnegative integer powers of the number two; in other words, two times itself a certain number of times. ... A Leyland number is an integer of the form xy + yx with 1 < x ≤ y. ... A Markov number or Markoff number is an integer x, y or z that is part of a solution to the Markov Diophantine equation The first few Markov numbers are 1, 2, 5, 13, 29, 34, 89, 169, 194, 233, 433, 610, 985, 1325, ... (sequence A002559 in OEIS) appearing in... 142,857 is the best-known cyclic number. ... In mathematics, a Kaprekar number is a number that, in a given base, when squared, can be split into two numbers with the same number of digits as the original number which add up to the original number again. ... A Harshad number, or Niven number, is an integer that is divisible by the sum of its digits in a given number base. ... 144,000 is a positive whole integer. ... In mathematics, a prime number of the form (2p + 1) / 3 for a prime number p is called a Wagstaff prime; they are related to the New Mersenne conjecture. ... A vampire number (or true vampire number) is a composite natural number v, with an even number of digits n, that can be factored into two integers x and y each with n/2 digits and not both with trailing zeroes, where v contains all the digits from x and... In mathematics, the Pell numbers and Companion Pell Numbers (Pell-Lucas Numbers) are both sequences of integers. ... Irreducible can refer to: irreducible (mathematics) irreducible (philosophy) This is a disambiguation page &#8212; a navigational aid which lists other pages that might otherwise share the same title. ... Group representation theory is the branch of mathematics that studies properties of abstract groups via their representations as linear transformations of vector spaces. ... In mathematics, the Monster group M is a group of order    246 · 320 · 59 · 76 · 112 · 133 · 17 · 19 · 23 · 29 · 31 · 41 · 47 · 59 · 71 = 808017424794512875886459904961710757005754368000000000 ≈ 8 · 1053. ... The Fourier series is a mathematical tool used for analyzing an arbitrary periodic function by decomposing it into a weighted sum of much simpler sinusoidal component functions sometimes referred to as normal Fourier modes, or simply modes for short. ... In mathematics, the j-invariant, regarded as a function of a complex variable &#964;, is a modular function defined on the upper half plane of complex numbers with positive imaginary part. ... In mathematics, monstrous moonshine is a term devised by John Horton Conway and Simon P. Norton in 1979, used to describe the (then totally unexpected) connection between the monster group M and modular functions (particularly, the j function). ... In combinatorial mathematics, the Catalan numbers form a sequence of natural numbers that occur in various counting problems, often involving recursively defined objects. ... In recreational mathematics, a repdigit is a natural number composed of repeated instances of the same digit, most often in the decimal numeral system. ... A Carol number, named after Carol G. Kirnon, is an integer of the form . ... An exponential factorial is a positive integer n raised to the power of n - 1, which in turn was raised to the power of n - 2, and so on and so forth, that is, . The exponential factorial can also be defined with the recurrence relation . ... A Kynéa number (pronounced: Ka-Nay), named after Kynéa R. Griffith, is an integer of the form . ... In mathematics, a Fermat number, named after Pierre de Fermat who first studied them, is a positive integer of the form where n is a nonnegative integer. ... An alternating factorial is the sum of the first n factorials with the odd-indexed factorials multiplied by −1 if n is even, and the even-indexed factorials multiplied by −1 if n is odd, resulting in an alternation of signs of the summands (or alternation of addition and subtraction... In mathematics, a sexy prime is a pair of prime numbers that differ by six; compare this with twin primes, pairs of prime numbers that differ by two, and cousin primes, pairs of prime numbers that differ by four. ... In mathematics, a unique prime is a certain kind of prime number. ... The n-th prime gap (short for prime number gap), denoted gn, is the difference between the n+1-th and n-th prime number, pn. ... A self-descriptive number is an integer m that in a given base b is b-digits long in which each digit d at position n (the most significant digit being at position 0 and the least significant at position b - 1) counts how many instances of digit n are... The beginning of the sequence of factorials (sequence A000142 in OEIS) In mathematics, the factorial of a number n is the product of all positive integers less than or equal to n. ... In mathematics, a Riesel number is an odd natural number k for which the integers of the form k*2n-1 are all composite. ... A Fibonacci prime is a Fibonacci number that is prime. ... In mathematics, a colossally abundant number (sometimes abbreviated as CA) is a certain kind of natural number. ...