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...

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...

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...

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...

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...

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...