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Class of natural numbers
In mathematics, a superabundant number is a kind of natural number. A natural number n is called superabundant precisely when, for all m < n: σ ( m ) m
Superabundant_number
Natural number
129,600 : 69th superabundant number, 100th highly composite number, 18th superior highly composite number 2,262,366,343,746 : number of trees with 35
1,000,000,000,000
Natural number
Pell number, 193rd Markov number 55,555,555,555,555 : repdigit 55,898,149,507,200 : 79th superabundant number 57,850,602,535,042 : 194th Markov number 58
10,000,000,000,000
Natural number
Markov number 130,429,015,516,800 : 82nd superabundant number 144,403,552,893,600 : 83rd superabundant number 145,624,636,022,689 : 206th Markov number 148
100,000,000,000,000
Type of natural number
abundant number. It is a stronger restriction than that of a superabundant number, but not strictly stronger than that of an abundant number. Formally
Colossally_abundant_number
Number equal to the sum of its proper divisors
In number theory, a perfect number is a positive integer that is equal to the sum of its positive proper divisors, that is, divisors excluding the number
Perfect_number
Number that is more than the sum of its proper divisors
classification only to the even numbers. Almost perfect number Amicable number Sociable number Superabundant number Prielipp (1970), Theorem 1, pp. 693–694. Prielipp
Deficient_number
Integer having a non-trivial divisor
A composite number is a positive integer that can be formed by multiplying two smaller positive integers. Accordingly, it is a positive integer that has
Composite_number
Natural number
divisors (excluding the number itself) 2040 > 840 It is an abundant number and also a superabundant number. It is an idoneal number. It is the least common
840_(number)
Number that is less than the sum of its proper divisors
of n is the ratio σ(n)/n. A number whose abundancy index is greater than any lower number is called a superabundant number (sequence A004394 in the OEIS)
Abundant_number
Number divisible only by 1 and itself
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that
Prime_number
Natural number
{\pi }{15}}} is expressible in terms of square roots. The first 15 superabundant numbers are the same as the first 15 colossally abundant numbers. There
15_(number)
Topics referred to by the same term
acceleration, in seismology and earthquake engineering Superabundant number, a type of number (mathematical concept) Surface area Unbarred spiral galaxy
SA
Number that is abundant but not semiperfect
In number theory, a weird number is a natural number that is abundant but not semiperfect. In other words, the sum of the proper divisors (divisors including
Weird_number
Natural number
Leyland number using 3 and 19 (319 + 193) 1,163,962,800 : smallest superabundant number that is not highly composite 1,166,732,814 : number of signed
1,000,000,000
Numbers obtained by adding the two previous ones
month, the number of pairs of rabbits is equal to the number of mature pairs (that is, the number of pairs in month n – 2) plus the number of pairs alive
Fibonacci_sequence
Number used for counting
natural-number results: subtracting a larger natural number from a smaller one results in a negative number and dividing one natural number by another
Natural_number
Odd number with specific properties
In number theory, a Sierpiński number is an odd natural number k such that k × 2 n + 1 {\displaystyle k\times 2^{n}+1} is composite for all natural numbers
Sierpiński_number
Area of a right triangle with rational-numbered sides
In number theory, a congruent number is a positive integer that is the area of a right triangle with three rational number sides. A more general definition
Congruent_number
Natural number
composite, superabundant, and the 5th colossally abundant number. It is also a sparsely totient number. 120 is also the smallest highly composite number with
120_(number)
Prime number of the form 2^n – 1
mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number of the form Mn = 2n − 1 for some integer
Mersenne_prime
Two or more natural numbers with a common abundancy index
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
Friendly_number
Product of two prime numbers
In number theory, 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
Semiprime
Figurate number
The triangular lattice representing the n {\displaystyle n} th triangular number contains n {\displaystyle n} rows: the first row contains one point, the
Triangular_number
Product of an integer with itself
In mathematics, a square number or perfect square is an integer that is the square of an integer; in other words, it is the product of some integer with
Square_number
Number that remains the same when its digits are reversed
A palindromic number (also known as a numeral palindrome or a numeric palindrome) is a number (such as 16361) that remains the same when its digits are
Palindromic_number
Natural number
893,615,154 = number of centered hydrocarbons with 32 carbon atoms 13,967,553,600 = superior highly composite number, superabundant number 14,182,439,040
10,000,000,000
Polyhedral number representing a tetrahedron
A tetrahedral number, or triangular pyramidal number, is a figurate number that represents a pyramid with a triangular base and three sides, called a tetrahedron
Tetrahedral_number
Positive integer of the form (2^(2^n))+1
In mathematics, a Fermat number, named after Pierre de Fermat (1601–1665), the first known to have studied them, is a positive integer of the form: F n
Fermat_number
Composite number in number theory
In number theory, a Carmichael number is a composite number n {\displaystyle n} which in modular arithmetic satisfies the congruence relation: b n
Carmichael_number
Integer having only small prime factors
In number theory, an n-smooth (or n-friable) number is an integer whose prime factors are all less than or equal to n. For example, a 7-smooth number is
Smooth_number
Type of figurate number
In mathematics, a polygonal number is a number that counts dots arranged in the shape of a regular polygon. These are one type of 2-dimensional figurate
Polygonal_number
Integer divisible by sum of its digits
In recreational mathematics, a Harshad number (or Niven number) in a given number base is an integer that is divisible by the sum of its digits when written
Harshad_number
Number of form 2^(2^p-1)-1 with prime exponent
In mathematics, a double Mersenne number is a Mersenne number of the form M M p = 2 2 p − 1 − 1 {\displaystyle M_{M_{p}}=2^{2^{p}-1}-1} where p {\displaystyle
Double_Mersenne_number
Number that when multiplied by another number moves its last digit to its front
In mathematics, an n-parasitic number (in base 10) is a positive natural number which, when multiplied by n, results in movement of the last digit of its
Parasitic_number
Figurate number
A pentagonal number is a figurate number that extends the concept of triangular and square numbers to the pentagon, but, unlike the first two, the patterns
Pentagonal_number
Numbers with a certain property involving recursive summation
In number theory, a happy number is a number which eventually reaches 1 when the number is replaced by the sum of the square of each digit. For instance
Happy_number
Number whose sums of distinct divisors represent all smaller numbers
In number theory, a practical number or panarithmic number is a positive integer n {\displaystyle n} such that all smaller positive integers can be represented
Practical_number
Square of a triangular number
In number theory, the sum of the first n cubes is the square of the nth triangular number. That is, 1 3 + 2 3 + 3 3 + ⋯ + n 3 = ( 1 + 2 + 3 + ⋯ + n ) 2
Squared_triangular_number
Numbers that evenly divide powers of 60
and have different names coming from their different areas of study. In number theory, these numbers are called 5-smooth, because they can be characterized
Regular_number
Type of integer in number theory
In number theory, a polite number is a positive integer that can be written as the sum of two or more consecutive positive integers. A positive integer
Polite_number
Number, product of consecutive integers
A pronic number is a number that is the product of two consecutive integers, that is, a number of the form n ( n + 1 ) {\displaystyle n(n+1)} . The study
Pronic_number
Base-dependent property of integers
In mathematics, a natural number in a given number base is a p {\displaystyle p} -Kaprekar number if the representation of its square in that base can
Kaprekar_number
Concept in number theory
In number theory, a narcissistic number (also known as a pluperfect digital invariant (PPDI), an Armstrong number (after Michael F. Armstrong) or a plus
Narcissistic_number
Numbers with many divisors
highly composite number is a positive integer that has more divisors than all smaller positive integers. If d(n) denotes the number of divisors of a positive
Highly_composite_number
Integer of the form 3 × 2^n – 1 for non-negative n
In number theory, a Thabit number, Thâbit ibn Qurra number, or 321 number is an integer of the form 3 ⋅ 2 n − 1 {\displaystyle 3\cdot 2^{n}-1} for a non-negative
Thabit_number
Number of the form (n * 2^n) - 1
number theory, a Woodall number (Wn) is any natural number of the form W n = n ⋅ 2 n − 1 {\displaystyle W_{n}=n\cdot 2^{n}-1} for some natural number
Woodall_number
Recursive integer sequence
they were previously discovered in the 1730s by Minggatu. The n-th Catalan number can be expressed directly in terms of the central binomial coefficients
Catalan_number
Number whose square ends in the same digits
In mathematics, an automorphic number (sometimes referred to as a circular number) is a natural number in a given number base b {\displaystyle b} whose
Automorphic_number
Number that represents a hexagon with a dot in the center
mathematics and combinatorics, a centered hexagonal number, or centered hexagon number, is a centered figurate number that represents a hexagon with a dot in the
Centered_hexagonal_number
Odd number with specific properties
In mathematics, a Riesel number is an odd natural number k for which k × 2 n − 1 {\displaystyle k\times 2^{n}-1} is composite for all natural numbers
Riesel_number
Numbers in a type of Lucas sequence
starts with 0 and 1, then each following number is found by adding the number before it to twice the number before that. The first Jacobsthal numbers
Jacobsthal_number
Number equal to the sum of all or some of its divisors
In number theory, a semiperfect number or pseudoperfect number is a natural number n equal to the sum of all or some of its proper divisors. A semiperfect
Semiperfect_number
Numbers whose sum of divisors is twice the number plus 1
unsolved problems in mathematics In mathematics, a quasiperfect number is a natural number n for which the sum of all its divisors (the sum-of-divisors function
Quasiperfect_number
Natural number whose divisor sum is greater than that of any smaller number
smaller number with larger sum of divisors, σ(360360) = 1572480, so 9! is not highly abundant. Alaoglu and Erdős noted that all superabundant numbers
Highly_abundant_number
Figurate number
A pyramidal number is the number of points in a pyramid with a polygonal base and triangular sides. The term often refers to square pyramidal numbers,
Pyramidal_number
Number of ways to pair up n objects
These numbers also describe the number of matchings (the Hosoya index) of a complete graph on n vertices, the number of permutations on n elements that
Telephone number (mathematics)
Telephone_number_(mathematics)
Number used to approximate the square root of 2
starts with 0 and 1, and then each Pell number is the sum of twice the previous Pell number, plus the Pell number before that. The first few terms of the
Pell_number
Size of a geometric arrangement of points
The term figurate number is used by different writers for members of different sets of numbers, generalizing from triangular numbers to different shapes
Figurate_number
Infinite integer series where the next number is the sum of the two preceding it
numbers two terms apart in the Fibonacci sequence results in the Lucas number in between. The first few Lucas numbers are 2, 1, 3, 4, 7, 11, 18, 29, 47
Lucas_number
Integer whose multiples are digit rotations
A cyclic number is an integer for which cyclic permutations of the digits are successive integer multiples of the number. The most widely known is the
Cyclic_number
Type of natural number
In number theory, a self number in a given number base b {\displaystyle b} is a natural number that cannot be written as the sum of any other natural
Self_number
Number whose divisors add to a multiple of that number
perfect number (also called multiperfect number or pluperfect number) is a generalization of a perfect number. For a given natural number k, a number n is
Multiply_perfect_number
Canadian-American mathematician of Greek origin and operations researcher (1914–1981)
the prime factorizations of superabundant numbers and highly composite numbers. In particular, for a highly abundant number n = ∏ i p k p {\displaystyle
Leonidas_Alaoglu
Number, non-palindrome after repeated sum with reverse
numbers exist? More unsolved problems in mathematics A Lychrel number is a natural number that cannot form a palindrome through the iterative process of
Lychrel_number
Type of composite number with an even number of digits
recreational mathematics, a vampire number (or true vampire number) is a composite natural number with an even number of digits, that can be factored into
Vampire_number
Type of number introduced by Mike Keith
mathematics, a Keith number or repfigit number (short for repetitive Fibonacci-like digit) is a natural number n {\displaystyle n} in a given number base b {\displaystyle
Keith_number
Number raised to the third power
algebra, the cube of a number n is its third power, that is, the result of multiplying three instances of n together. The cube of a number n is denoted n3,
Cube_(algebra)
Number of stacked spheres in a pyramid
In mathematics, a pyramid number, or square pyramidal number, is a natural number that counts the stacked spheres in a pyramid with a square base. The
Square_pyramidal_number
Mathematical integer sequence
mathematics, the Schröder number S n , {\displaystyle S_{n},} also called a large Schröder number or big Schröder number, describes the number of lattice paths
Schröder_number
Composite number with special property
In number theory, an n-Knödel number for a given positive integer n is a composite number m with the property that each i < m coprime to m satisfies i
Knödel_number
Type of Poulet number
In number theory, a super-Poulet number is a Poulet number, or pseudoprime to base 2, whose every divisor d {\displaystyle d} divides 2 d − 2 {\displaystyle
Super-Poulet_number
Numbers that contain only the digit 1
In recreational mathematics, a repunit is a number like 11, 111, or 1111 that contains only the digit 1 — a more specific type of repdigit. The term stands
Repunit
Integer filtered out using a sieve similar to that of Eratosthenes
In number theory, a lucky number is a natural number in a set which is generated by a certain "sieve". This sieve is similar to the sieve of Eratosthenes
Lucky_number
Number of paths between grid corners, allowing diagonal steps
In mathematics, a Delannoy number D {\displaystyle D} counts the paths from the southwest corner (0, 0) of a rectangular grid to the northeast corner (m
Delannoy_number
Number that has fewer digits than the number of digits in its prime factorization
In number theory, an extravagant number (also known as a wasteful number) is a natural number in a given number base that has fewer digits than the number
Extravagant_number
Concatenation of the first n prime numbers
In mathematics, a Smarandache–Wellin number is an integer that in a given base is the concatenation of the first n prime numbers written in that base.
Smarandache–Wellin_number
Numbers parameterizing ways to partition a set
particularly in combinatorics, a Stirling number of the second kind (or Stirling partition number) is the number of ways to partition a set of n objects
Stirling numbers of the second kind
Stirling_numbers_of_the_second_kind
Number in the 5th cell of any row of Pascal's triangle
In number theory, a pentatope number (or hypertetrahedral number or triangulo-triangular number) is a number in the fifth cell of any row of Pascal's
Pentatope_number
Natural number with a decimal representation made of repeated instances of the same digit
or sometimes monodigit is a natural number composed of repeated instances of the same digit in a positional number system (often implicitly decimal). The
Repdigit
Integer whose representation contains every digit in its number base
In mathematics, a pandigital number is an integer that in a given base has among its significant digits each digit used in the base at least once. For
Pandigital_number
Two raised to an integer power
A power of two is a number of the form 2n where n is an integer, that is, the result of exponentiation with the number two as the base and integer n as
Power_of_two
Type of positive integer
In number theory, a positive integer k is said to be an Erdős–Woods number if it has the following property: there exists a positive integer a such that
Erdős–Woods_number
Positive integer whose divisors have a harmonic mean that is an integer
In mathematics, a harmonic divisor number or Ore number is a positive integer whose divisors have a harmonic mean that is an integer. The first few harmonic
Harmonic_divisor_number
23# × 11 × 7 × 52 × 34 × 28 ≈ 6.6737×10153 is the largest number that is both superabundant and highly composite. Mathematics: 2521 − 1 ≈ 8.8648×10156
Orders_of_magnitude_(numbers)
Function whose domain is the positive integers
log e ( x ) {\displaystyle \log _{e}(x)} . In number theory, an arithmetic, arithmetical, or number-theoretic function is generally any function whose
Arithmetic_function
Positive integer with large prime factors
A k-rough number, as defined by Finch in 2001 and 2003, is a positive integer whose prime factors are all greater than or equal to k. k-roughness has alternately
Rough_number
Arithmetic function related to the divisors of an integer
are an infinite number of values of n that violate the inequality, and it is known that the smallest such n > 5040 must be superabundant (Akbary & Friggstad
Divisor_function
Class of natural numbers with many divisors
In number theory, a superior highly composite number is a natural number which, in a particular rigorous sense, has many divisors. Particularly, it is
Superior highly composite number
Superior_highly_composite_number
Type of figurate number
A nonagonal number, or an enneagonal number, is a figurate number that extends the concept of triangular and square numbers to the nonagon (a nine-sided
Nonagonal_number
Integer that is both a perfect square and a triangular number
mathematics, a square triangular number (or triangular square number) is a number which is both a triangular number and a square number, in other words, the sum
Square_triangular_number
Number of the form x^y + y^x
In number theory, a Leyland number is a number of the form x y + y x {\displaystyle x^{y}+y^{x}} where x and y are integers greater than 1. They are named
Leyland_number
Decomposition of a number into a product
composite number, or it is not, in which case it is a prime number. For example, 15 is a composite number because 15 = 3 · 5, but 7 is a prime number because
Integer_factorization
Mathematical concept
Cullen number is a member of the integer sequence C n = n ⋅ 2 n + 1 {\displaystyle C_{n}=n\cdot 2^{n}+1} (where n {\displaystyle n} is a natural number). Cullen
Cullen_number
Number n where the highest prime factor of (n^2 + 1) is at least 2n
In mathematics, a Størmer number or arc-cotangent irreducible number is a positive integer n {\displaystyle n} for which the greatest prime factor of n
Størmer_number
Mathematical concept in prime numbers
power. In particular, a number that has two distinct representations as a sum of two squares is composite. Every idoneal number generates a set containing
Idoneal_number
Product of prime numbers, plus one
there are infinitely many prime numbers. A Euclid number of the second kind (also called Kummer number) is an integer of the form En = pn # − 1, where pn #
Euclid_number
Class of series of figurate numbers, each having a central dot
k-gonal number contains k more dots than the previous layer. Each centered k-gonal number in the series is k times the previous triangular number, plus
Centered_polygonal_number
Number that is the result of operation on its own digits
A Friedman number is an integer, which represented in a given numeral system, is the result of a non-trivial expression using all its own digits in combination
Friedman_number
Numbers whose prime factors all divide the number more than once
every prime number p dividing m, p2 also divides m. Equivalently, a powerful number is the product of a square and a cube, that is, a number m of the form
Powerful_number
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