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...

& 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...

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...

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...

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...

(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...

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...

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...

*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...

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...

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 range of Euler's totient function φ, that is, the equation φ(x) = n has no solution...

{\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...

{\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 (...

{\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...

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

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)...

is Tn−1. The function T is the additive analog of the factorial function, which is the products of integers from 1 to n. This same function was coined as...

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),...

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...

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

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...

{p^{\alpha }}}} where ϕ ( n ) {\displaystyle \phi (n)} is the Euler's totient function. The Euler numbers grow quite rapidly for large indices as they have...

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 )...

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

ideal system of coins. In number theory, all powers of three are perfect totient numbers. The sums of distinct powers of three form a Stanley sequence,...

d}\right)\alpha ^{d},} where φ {\displaystyle \varphi } is Euler's totient function. The necklace polynomials M ( α , n ) {\displaystyle M(\alpha ,n)}...