The Euler $\phi $ function for generalized integers
نویسندگان
چکیده
منابع مشابه
Arithmetic Functions and the Euler Phi Function
• An arithmetic function takes positive integers as inputs and produces real or complex numbers as outputs. • If f is an arithmetic function, the divisor sum Df(n) is the sum of the values of f at the positive divisors of n. • τ (n) is the number of positive divisors of n; σ(n) is the sum of the positive divisors of n. • The Möbius function μ(n) is 1 if n = 1 and 0 if n has a repeated prime fac...
متن کاملEuler ’ s Phi Function and Graph Labeling
A graph G(V,E) with vertex set V is said to have a prime labeling if there exist a bijection f : V (G) → {1, 2, . . . , |V |} such that for each edge xy ∈ E(G), f(x) and f(y) are relatively prime. It becomes an interesting problem to investigate the maximum possible edges that can be constructed in a graph with n vertices having prime labeling property. We interpret this problem in number theor...
متن کاملA Measure of the Nonmonotonicity of the Euler Phi Function
ure of the nonmonotonicity of f. In particular, F is identically zero if and only if f is strictly increasing . Here we shall take f to be (p, Euler's function, and study the associated function F 4„ which we henceforth call F. We shall show that F(n)/n is asymptotically representable as a function of T(n)/n . Then we shall prove that F(n)/n has a distribution function. We shall study max,,, F(...
متن کاملEuler-type transformations for the generalized hypergeometric function
Abstract We provide generalizations of two of Euler’s classical transformation formulas for the Gauss hypergeometric function extended to the case of the generalized hypergeometric function r+2Fr+1(x) when there are additional numeratorial and denominatorial parameters differing by unity. The method employed to deduce the latter is also implemented to obtain a Kummer-type transformation formula...
متن کاملOn generalized Hermite-Hadamard inequality for generalized convex function
In this paper, a new inequality for generalized convex functions which is related to the left side of generalized Hermite-Hadamard type inequality is obtained. Some applications for some generalized special means are also given.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1963
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1963-0152489-0