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totient function

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  • Euler's totient function — For other functions named after Euler, see List of topics named after Leonhard Euler. The first thousand values of φ(n) In number theory, the totient φ(n) of a positive integer n is defined to be the number of positive integers less than or equal …   Wikipedia

  • Proofs involving the totient function — This page provides proofs for identities involving the totient function varphi(k) and the Möbius function mu(k).um of integers relatively prime to and less than or equal to n Claim::sum {1le kle n atop {gcd(k,n)=1 k = frac{1}{2} , varphi(n) ,… …   Wikipedia

  • Carmichael's totient function conjecture — In mathematics, Carmichael s totient function conjecture concerns the multiplicity of values of Euler s totient function phi;( n ), which counts the number of integers less than and coprime to n .This function phi;( n ) is equal to 2 when n is… …   Wikipedia

  • Jordan's totient function — In number theory, Jordan s totient function J k(n) of a positive integer n is the number of k tuples of positive integers all less than or equal to n that form a coprime ( k + 1) tuple together with n . This is a generalisation of Euler s totient …   Wikipedia

  • Euler's totient function — noun A function that counts how many integers below a given integer are coprime to it …   Wiktionary

  • totient — noun The number of positive integers not more than a specified integer that are relatively prime to it. See Also: Eulers totient function …   Wiktionary

  • Arithmetic function — In number theory, an arithmetic (or arithmetical) function is a real or complex valued function ƒ(n) defined on the set of natural numbers (i.e. positive integers) that expresses some arithmetical property of n. [1] An example of an arithmetic… …   Wikipedia

  • Perfect totient number — In number theory, a perfect totient number is an integer that is equal to the sum of its iterated totients. That is, we apply the totient function to a number n , apply it again to the resulting totient, and so on, until the number 1 is reached,… …   Wikipedia

  • Highly totient number — A highly totient number k is an integer that has more solutions to the equation φ( x ) = k , where φ is Euler s totient function, than any integer below it. The first few highly totient numbers are1, 2, 4, 8, 12, 24, 48, 72, 144, 240, 432, 480,… …   Wikipedia

  • Divisor function — σ0(n) up to n = 250 Sigma function σ …   Wikipedia

  • Sparsely totient number — In mathematics, a sparsely totient number is a certain kind of even natural number. A natural number, n , is sparsely totient if for all m > n , : phi;( m )> phi;( n ), where phi; is Euler s totient function. The first few sparsely totient… …   Wikipedia

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