Integer sequences

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

numbers of the form 2^{2^p-1}-1, where p and 2^p-1 are prime numbers

a number all of whose prime factors are small

one of certain constant-recursive integer sequences

numbers with a perfect number of factors and a perfect sum of factors

theorem

maximum number of regions into which a cube can be partitioned by n cuts

the sum of the first n cubes, which equals the square of the nth triangular number

natural number sharing its abundancy index with at least one other number

an integer n that is divisible by the count of its divisors

positive integer whose divisors have a harmonic mean that is an integer

number that is one more than the product of the first n prime numbers

pairs of positive integers such that the sum of the proper divisors of either number is one more than the other number

In number theory, a nontotient is a positive integer n which is not a totient number: it is not in the image of Euler's totient function φ, that is, the equation φ(x) = n has no solution x. In other words, n is a nontotient if there is no integer x that has exactly n coprimes below it. All odd numbers are nontotients, except 1, since it has the solutions x = 1 and x = 2. The first few even nontotients are this sequence:

Sequence of integers

positive integer which equals half of the sum of the divisors of the sum of its divisors

prime number that is product of first n primes ± 1

member of an integer sequence in which each number is the sum of a unique pair of earlier numbers

number of permutations of the numbers from 1 to n in which m elements are greater than the previous element

sequence of integers

the smallest integer which yields a prime number when added to a given primorial

a sequence of integers formed by rounding down the integer multiples of a positive irrational number

a type of integer with many divisors

result of multiplying five instances of a natural number together

sequence of numbers with distinct sums

class of binary number

concept in mathematics

the smallest number whose sum of divisors exceeds some given bound

mathematical integer sequence

number of paths between grid corners, allowing diagonal steps

number with odd number of 1s in binary

constant used in a magic square

numbers giving a solution to several counting problems in combinatorics

Mathematical concept in prime numbers

natural number n whose largest prime factor is strictly greater than √n

result of the term-by-term multiplication of a geometric progression with the corresponding terms of an arithmetic progression

result of multiplying six instances of a number

number with a half-integer abundancy index

a number k s.t. phi(x) = k has more solutions than for any lower number

a number k where p|k implies p + 1|k + 1 for primes p

natural number which is the length of an interval of consecutive integers such that every element has a factor in common with one of the endpoints

positive integer n for which the greatest prime factor of n2 + 1 is greater than or equal to 2n

natural number n for which the equality n=1+k(σ(n)−n−1) holds for some k

natural number which, in a particular rigorous sense, has many divisors

In mathematics, and more specifically number theory, the hyperfactorial of a positive integer n is the product of the numbers of the form x^x from 1^1 to

product of two distinct primes which are congruent to 3 modulo 4

tree in which the vertices correspond 1-for-1 to the positive rational numbers

one part of a particular Lucas sequence

recursive mathematical formula

numbers that evenly divide powers of 60

composite number n such that p divides n/p − 1 for every prime divisor p of n

positive integer of the form (4n + 1)

endless sequence

In mathematics, and more specifically number theory, the superfactorial of a positive integer n is the product of the first n factorials. They are a special case of the Jordan–Pólya numbers, which are products of arbitrary collections of factorials.

integer which is the sum of its positive proper unitary divisors, not including the number itself

the problem of finding sets of integers in which each is a proper divisor of one plus the product of the others

natural number above 1 which is a cototient to more numbers than any lower number

positive integer that can be written as the sum of two or more consecutive positive integers

abundant number whose proper divisors are all deficient numbers

one of a set of numbers that Dijkstra used to explain smoothsort