Searches , social queries for CARMICHAEL NUMBER
Search references for CARMICHAEL NUMBER. Phrases containing CARMICHAEL NUMBER
See searches and references containing CARMICHAEL NUMBER!
Search references for CARMICHAEL NUMBER. Phrases containing CARMICHAEL NUMBER
See searches and references containing CARMICHAEL NUMBER!CARMICHAEL 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
Type of positive composite integer
In mathematics, a Lucas–Carmichael number is a positive composite integer n such that If p is a prime factor of n, then p + 1 is a factor of n + 1; n
Lucas–Carmichael_number
Numbers obtained by adding the two previous ones
F6 and F12) every Fibonacci number has a prime factor that is not a factor of any smaller Fibonacci number (Carmichael's theorem). As a result, 8 and
Fibonacci_sequence
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
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
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
Natural number
Carmichael number. 561 is considered one since it satisfies the Korselt’s Criterion. A number satisfies the criterion if the number is an odd number,
561_(number)
Composite number which passes Miller–Rabin primality test
which there exist numbers that are pseudoprimes to all coprime bases (the Carmichael numbers), there are no composites that are strong pseudoprimes to all
Strong_pseudoprime
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
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
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
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
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
Topics referred to by the same term
Saskatchewan Carmichael number, a special kind of number in number theory named for mathematician Robert Carmichael Carmichael, Saskatchewan, Canada Carmichael, South
Carmichael
Positive integer of the form (2^(2^n))+1
doi:10.2307/2031878, JSTOR 2031878 Yabuta, M. (2001), "A simple proof of Carmichael's theorem on primitive divisors" (PDF), Fibonacci Quarterly, 39 (5): 439–443
Fermat_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
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
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
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
Natural number
× 31. It is a Lucas–Carmichael number. 2016 = 25 × 32 × 7. It is the second-smallest Erdős–Nicolas numberand a triangular number. 2017 is a sexy prime
2000_(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
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
Natural number
composite number, the first nontrivial taxicab number, a Carmichael number, and a centered cube number. It is also the smallest absolute Euler pseudoprime
1729_(number)
Number that is less than the sum of its proper divisors
In number theory, an abundant number or excessive number is a positive integer for which the sum of its proper divisors is greater than the number. The
Abundant_number
Type of figurate number
A hexagonal number is a figurate number. The nth hexagonal number hn is the number of distinct dots in a pattern of dots consisting of the outlines of
Hexagonal_number
Number of unique ways to draw non-intersecting chords in a circle
In mathematics, the nth Motzkin number is the number of different ways of drawing non-intersecting chords between n points on a circle (not necessarily
Motzkin_number
American mathematician (1879–1967)
are not primes), Carmichael's totient function conjecture, Carmichael's theorem, and the Carmichael function, all significant in number theory and in the
Robert_Daniel_Carmichael
Natural number
Friedman number 100,489 = 3172, the smallest 6-digit square 101,101 = smallest palindromic Carmichael number 101,723 = smallest prime number whose square
100,000
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
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
Type of composite number
number. Unsolved problem in mathematics Are there infinitely many Giuga numbers? Is there a composite Giuga number that is also a Carmichael number?
Giuga_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
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
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
Ten raised to an integer power
the number ten; in other words, ten multiplied by itself a certain number of times (when the power is a positive integer). By definition, the number one
Power_of_10
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
Number that has a perfect number of factors adding up to another perfect number
In number theory, a sublime number is a positive integer which has a perfect number of positive factors (including itself), and whose positive factors
Sublime_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
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
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
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
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
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
Iterative algorithm on numbers
In number theory, Kaprekar's routine is an iterative algorithm named after its inventor, Indian mathematician D. R. Kaprekar. Each iteration starts with
Kaprekar's_routine
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
Class of binary number
In number theory, an evil number is a non-negative integer that has an even number of 1s in its binary expansion. These numbers give the positions of
Evil_number
Integer where the average of its positive divisors is also an integer
In number theory, an arithmetic number is an integer for which the average of its positive divisors is also an integer. For instance, 6 is an arithmetic
Arithmetic_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
Natural number
Markov number 51984 = 2282 = 373 + 113, the smallest square to the sum of only five distinct fourth powers. 52488 = 3-smooth number 52633 = Carmichael number
50,000
Number whose divisors summed twice over equal twice itself
In number theory, a superperfect number is a positive integer n that satisfies σ 2 ( n ) = σ ( σ ( n ) ) = 2 n , {\displaystyle \sigma ^{2}(n)=\sigma (\sigma
Superperfect_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 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
Concept in combinatorics
In mathematics, the cake number, denoted by Cn, is the maximum of the number of regions into which a 3-dimensional cube can be partitioned by exactly
Cake_number
Type of composite integer
In number theory, a Smith number is a composite number for which, in a given number base, the sum of its digits is equal to the sum of the digits in its
Smith_number
Natural number
10570 = weird number 10585 = Carmichael number 10601 = palindromic prime in bases 10 (1060110) and 30 (BNB30) 10609 = 1032, tribonacci number 10631 = palindromic
10,000
Function in mathematical number theory
In number theory, a branch of mathematics, the Carmichael function λ(n) of a positive integer n is the smallest positive integer m such that a m ≡ 1 (
Carmichael_function
Integer named after Reo Fortune
(Fortune's conjecture) More unsolved problems in mathematics In number theory, a Fortunate number is the smallest integer m > 1 {\displaystyle m>1} such that
Fortunate_number
Natural number
sphenic number, a Lucas–Carmichael number, and a Harshad number. 936 = 23 × 32 × 13. It is a pentagonal pyramidal number and a Harshad number. 937 is
900_(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
Positive integer that is the product of three distinct prime numbers
In number theory, a sphenic number (from Ancient Greek: σφήν, 'wedge') is a positive integer that is the product of three distinct prime numbers. For
Sphenic_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
Mathematical sequences in combinatorics
frequently arise in combinatorics. Moreover, all three can be defined as the number of partitions of n elements into k non-empty subsets, where each subset
Stirling_number
Number that cannot be written as an aliquot sum
In mathematics, an untouchable number is a positive integer that cannot be expressed as the sum of all the proper divisors of any positive integer. That
Untouchable_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
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
Numeral ambigram
A strobogrammatic number is a number whose numeral is rotationally symmetric, so that it appears the same when rotated by 180 degrees. In other words,
Strobogrammatic_number
Property of a number
In mathematics, the persistence of a number is the number of times one must apply a given operation to an integer before reaching a fixed point at which
Persistence_of_a_number
Positive integer of the form 4n + 1
In number theory, a branch of mathematics, a Hilbert number is a positive integer of the form 4n + 1 (Flannery & Flannery (2000, p. 35)). The Hilbert numbers
Hilbert_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
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
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
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
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
Integers occurring in the coefficients of the Taylor series of 1/cosh t
combinatorics, specifically when counting the number of alternating permutations of a set with an even number of elements. The odd-indexed Euler numbers
Euler_number
Natural number
Lucas–Carmichael number. "A000217 - OEIS". oeis.org. Retrieved 2024-11-28. Sloane, N. J. A. (ed.). "Sequence A014105 (second hexagonal number)". The
300_(number)
Centered figurate number
In mathematics, a star number is a centered figurate number, a centered hexagram (six-pointed star), such as the Star of David, or the board Chinese checkers
Star_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
Count of the possible partitions of a set
2,5,15,52,203,877,4140,\dots } (sequence A000110 in the OEIS). The Bell number B n {\displaystyle B_{n}} counts the different ways to partition a set that
Bell_number
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
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
Probable prime that is composite
pseudoprime to all values of a that are coprime to x is called a Carmichael number. Catalan pseudoprime Elliptic pseudoprime Euler pseudoprime Euler–Jacobi
Pseudoprime
Numbers k where x - phi(x) = k has many solutions
In number theory, a branch of mathematics, a highly cototient number is a positive integer k {\displaystyle k} which is above 1 and has more solutions
Highly_cototient_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
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
perfect totient number 6563 – Sophie Germain prime 6581 – Sophie Germain prime 6599 – safe prime 6601 – Carmichael number, decagonal number, sum of the first
6000_(number)
Integer divisible by the number of its divisors
A refactorable number or tau number is an integer n that is divisible by the count of its divisors, or to put it algebraically, n is such that τ ( n )
Refactorable_number
Number that is the sum of its iterated totients
In number theory, a perfect totient number is an integer that is equal to the sum of its iterated totients. That is, one applies the totient function
Perfect_totient_number
Natural number
Pentagonal number, and a Hexagonal number. 40804 = palindromic square 41041 = Carmichael number 41472 = 3-smooth number, number of reduced trees with 24 nodes
40,000
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
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
Natural number
also the second-smallest Carmichael number, after 561, one of the first four Carmichael numbers identified by R. D. Carmichael in his 1910 paper introducing
1105_(number)
Abundant number whose proper divisors are all deficient numbers
primitive abundant number is an abundant number whose proper divisors are all deficient numbers. For example, 20 is a primitive abundant number because: The
Primitive_abundant_number
Polynomial sequence
In combinatorics, the Eulerian number A ( n , k ) {\textstyle A(n,k)} is the number of permutations of the numbers 1 to n {\textstyle n} in which exactly
Eulerian_number
Integer describing itself
In mathematics, a self-descriptive number is an integer m in a given base b that is b digits long, and each digit d at position n (the most significant
Self-descriptive_number
Trinbagonian-American activist (1941–1998)
(/ˈkwɑːmeɪ ˈtʊəreɪ/ KWAH-may TOOR-ay; born Stokely Standiford Churchill Carmichael; June 29, 1941 – November 15, 1998) was a Trinidadian-American activist
Stokely_Carmichael
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 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)
Type of number
In mathematics, and particularly in number theory, N is a primary pseudoperfect number if it satisfies the Egyptian fraction equation 1 N + ∑ p | N 1 p
Primary_pseudoperfect_number
Number sequence 3,0,2,3,2,5,5,7,10,...
reduces the number of restricted pseudoprimes for each sequence by roughly one-third and is especially efficient in detecting Carmichael numbers. The
Perrin_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
travel, tourism, insurance
CARMICHAEL NUMBER
CARMICHAEL NUMBER
CARMICHAEL NUMBER
CARMICHAEL NUMBER
CARMICHAEL NUMBER
CARMICHAEL NUMBER
CARMICHAEL NUMBER
CARMICHAEL NUMBER
CARMICHAEL NUMBER
travel, tourism, insurance