theory, Jordan's totient function, denoted as J k ( n ) {\displaystyle J_{k}(n)} , where k {\displaystyle k} is a positive integer, is a function of a positive...

In number theory, Euler's totient function counts the positive integers up to a given integer n that are relatively prime to n. It is written using the...

known as Carmichael's λ function, the reduced totient function, and the least universal exponent function. The order of the multiplicative group of integers...

ϕ {\displaystyle \phi } is Euler's totient function, than any integer smaller than it. The first few highly totient numbers are 1, 2, 4, 8, 12, 24, 48...

& Wright, Thm. 263 Hardy & Wright, Thm. 63 see references at Jordan's totient function Holden et al. in external links The formula is Gegenbauer's Hardy...

\ldots .} Here pn# is the primorial sequence and Jk is Jordan's totient function. The function ζ can be represented, for Re(s) > 1, by the infinite series...

(m)>\varphi (n)} where φ {\displaystyle \varphi } is Euler's totient function. The first few sparsely totient numbers are: 2, 6, 12, 18, 30, 42, 60, 66, 90, 120...

Using Lambert series, if J s ( n ) {\displaystyle J_{s}(n)} is Jordan's totient function, then ∑ n = 1 ∞ z n J − s ( n ) 1 − z n = Li s ⁡ ( z ) . {\displaystyle...

{\displaystyle k} and above 1. Here, ϕ {\displaystyle \phi } is Euler's totient function. There are infinitely many solutions to the equation for k {\displaystyle...

*1)^{2}} J k ∗ 1 = Id k {\displaystyle J_{k}*1={\text{Id}}_{k}} , Jordan's totient function. ( Id s J r ) ∗ J s = J s + r {\displaystyle...

Riemann zeta function at positive integers greater than one can be expressed by using the primorial function and Jordan's totient function Jk(n): ζ ( k...

theorem on composition series is a basic result. Jordan's theorem on finite linear groups Jordan's work did much to bring Galois theory into the mainstream...

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 to a number n...

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...

orthogonal basis. Ramanujan, On Certain Arithmetical Functions Nicol, p. 1 This is Jordan's totient function, Js(n). Cf. Hardy & Wright, Thm. 329, which states...

factors of n {\displaystyle n} (see prime omega function), J t {\displaystyle J_{t}} is Jordan's totient function, and d ( n ) = σ 0 ( n ) {\displaystyle d(n)=\sigma...

lists a few identities involving the divisor functions Euler's totient function, Euler's phi function Refactorable number Table of divisors Unitary divisor...

899 and preceding 901. It is the square of 30 and the sum of Euler's totient function for the first 54 positive integers. In base 10, it is a Harshad number...

with the factorial function, a product whose factors are the integers from 1 to n, Donald Knuth proposed the name Termial function, with the notation...

integers below it. That is, m − φ(m) = n, where φ stands for Euler's totient function, has no solution for m. The cototient of n is defined as n − φ(n),...

38 into nonprime parts 806 = 2 × 13 × 31, sphenic number, nontotient, totient sum for first 51 integers, happy number, Phi(51) 807 = 3 × 269, antisigma(42)...

Riordan number, area code for New Hampshire 604 = 22 × 151, nontotient, totient sum for first 44 integers, area code for southwestern British Columbia...

{\displaystyle \mathbb {F} _{q},} where φ {\displaystyle \varphi } is Euler's totient function. In F q , {\displaystyle \mathbb {F} _{q},} the freshman's dream identity...

_{1}(n)=2n} where σ 1 {\displaystyle \sigma _{1}} is the sum-of-divisors function. This definition is ancient, appearing as early as Euclid's Elements (VII...

number 1: for instance, the formulas for Euler's totient function or for the sum of divisors function are different for prime numbers than they are for 1...

its conjugate. The related function z ↦ − s ( − 1 / z ) {\textstyle z\mapsto -s\left(-1/z\right)} is the generating function for the negafibonacci numbers...

omega functions Almost prime Semiprime Euler's totient function Highly cototient Highly totient Noncototient Nontotient Perfect totient Sparsely totient Aliquot...

In mathematics, Hooley's delta function ( Δ ( n ) {\displaystyle \Delta (n)} ), also called Erdős--Hooley delta-function, defines the maximum number of...

{\displaystyle \varphi } is the totient function. The generalization to higher orders via ratios of Jordan's totient is ψ k ( n ) = J 2 k ( n ) J k (...

1 ) 2 x = 1 {\displaystyle \mu (n)=(-1)^{2x}=1} (where μ is the Möbius function and x is half the total of prime factors), while for the former μ ( n )...