Integer sequences

A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.

In mathematics, and more particularly in number theory, primorial is a function from natural numbers to natural numbers similar to the factorial function, but rather than successively multiplying positive integers, only prime numbers are multiplied.

Amicable numbers are two different numbers so related that the sum of the proper divisors of each is equal to the other number.

In mathematics, any of the positive integers that occurs as a coefficient in the binomial theorem is a binomial coefficient.

In mathematics, the factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n.

In mathematics, the Fibonacci numbers are the numbers in the following integer sequence, called the Fibonacci sequence, and characterized by the fact that, every number after the first two is the sum of the two preceding ones: Often, especially in modern usage, the sequence is extended by one more initial term: .

The term figurate number is used by different writers for members of different sets of numbers, generalizing from triangular numbers to different shapes (polygonal numbers) and different dimensions (polyhedral numbers).

In mathematics, the Lucas sequences and are certain constant-recursive integer sequences that satisfy the recurrence relation where and are fixed integers.

In number theory, a perfect number is a positive integer that is equal to the sum of its proper positive divisors, that is, the sum of its positive divisors excluding the number itself (also known as its aliquot sum).

A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.

The Lucas numbers or Lucas series are an integer sequence named after the mathematician François Édouard Anatole Lucas (1842–91), who studied both that sequence and the closely related Fibonacci numbers.

In number theory, a regular prime is a special kind of prime number, defined by Ernst Kummer in 1850 to prove certain cases of Fermat's Last Theorem.

In recreational mathematics a juggler sequence is an integer sequence that starts with a positive integer a0, with each subsequent term in the sequence defined by the recurrence relation:

In number theory, a lucky number is a natural number in a set which is generated by a certain "sieve".

In combinatorics, the Eulerian number A(n, m), is the number of permutations of the numbers 1 to n in which exactly m elements are greater than the previous element (permutations with m "ascents").

In number theory, friendly numbers are two or more natural numbers with a common abundancy, the ratio between the sum of divisors of a number and the number itself.

Regular numbers are numbers that evenly divide powers of 60 (or, equivalently powers of 30).

A Wolstenholme number is a number that is the numerator of the generalized harmonic number Hn,2.

A Fortunate number, named after Reo Fortune, for a given positive integer n is the smallest integer m > 1 such that pn# + m is a prime number, where the primorial pn# is the product of the first n prime numbers.

In recreational mathematics, a ban number is a number that does not contain a particular letter when spelled out in English; in other words, the letter is "banned.

In mathematics, especially order theory, a weak ordering is a mathematical formalization of the intuitive notion of a ranking of a set, some of whose members may be tied with each other.