Integer sequences

positive integer with exactly two divisors, 1 and itself

positive integer that has at least one positive divisor other than 1 or itself

positive integer which equals the sum of all its divisors

prime number of the form 2ⁿ−1

product of some integer with itself

pair of integers related by their divisors

figurate number

family of positive integers that occur as coefficients in the binomial theorem

number for which the sum of its proper divisors is greater than the number itself

entire infinite integer series where the next number is the sum of the two preceding it (0,1,1,2,3,5,8,13,21,...)

conjecture in mathematics that concerns sequences

positive integer of the form (2^(2^n))+1

recursive integer sequence

online database of integer sequences

rational number sequence 𝐵ₖ such that (𝑚+1)∑𝑛ᵐ=(ᵐ⁺¹₀)𝐵₀𝑛ᵐ⁺¹−(ᵐ⁺¹₁)𝐵₁𝑛ᵐ+(ᵐ⁺¹₂)𝐵₂𝑛ᵐ¯¹−(ᵐ⁺¹₃)𝐵₃𝑛ᵐ¯²+⋯

natural integer number for which the sum of its proper strict divisors (other than itself) is less than the number itself

number of protons or neutrons that make a nucleus particularly stable

product of a number being raised to the third power

In mathematics, a semiprime is a natural number that is the product of exactly two prime numbers. The two primes in the product may equal each other, so the semiprimes include the squares of prime numbers. Because there are infinitely many prime numbers, there are also infinitely many semiprimes. Semiprimes are also called biprimes, since they include two primes, or second numbers, by analogy with how "prime" means "first". Alternatively semiprimes are called almost-prime numbers, specifically the "2-almost-prime" biprime and "3-almost-prime" triprime.

two raised to an integer power

In mathematics, and more particularly in number theory, primorial, denoted by "p_{n}\#", 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.

integer that cannot be divided by a square number

integer sequence counting the possible partitions of a set

member of the set of triangular numbers, polygonal numbers, or polyhedral numbers

composite number in number theory

number in the Lucas sequence where each number is the sum of the two preceding it (2, 1, 3, 4, 7, 11, ...)

thumb|305px|Number of possible permutations and derangements of elements. ( factorial) is the number of -permutations; ( subfactorial) is the number of derangements – -permutations where all of the elements change their initial places.

integer filtered out using a sieve similar to that of Eratosthenes

positive integer with more divisors than any smaller positive integer has

positive integer that is the product of three distinct prime numbers

numbers whose aliquot sums form a cyclic sequence

number of the form n*(2^n)+1

unique real number solution to the equation x^3-x-1=0

ordered succession of integers, defined by a formula, recurrence, or property of its members

hypothetical number whose sum of divisors is twice the number plus 1

ten raised to an integer power

figurate number

positive integer that is an integer power of another positive integer

abundant number that is not semiperfect

integer sequence defined by the Taylor series expansion of the hyperbolic secant function and also appearing in that of the secant function

a natural number nontrivially representable in the form x^y + y^x

prime numbers of the form n!±1

denominator of close rational approximation to the square root of 2

important functions in combinatorics

number of patterns of non-intersecting chords with a given number of endpoints on a circle

positive integer that equals the sum of some of its proper divisors

natural number with a given number of prime factors

a number that is powerful but not a perfect power

subclass of centered polygonal number

integer that is both a perfect square and a triangular number

positive integer unexpressable as the sum of all proper divisors of any other integer

integer where each prime number dividing it can be squared to still divide it

product of all the integers from 1 up to the integral input of the function that have the same parity as this input

positive integer power of a prime number

result of multiplying four instances of a natural number together

natural number of the form n2^n − 1

natural number whose proper divisors sum to one less than itself

integer of the form 3 · 2ⁿ - 1 for non-negative n

Number sequence 3,0,2,3,2,5,5,7,10,... defined by recurrence relation P(n) = P(n-2) + P(n-3).

integer sequence in which each member of the sequence is the product of the previous members, plus one