On a sequence related to the coprime integers

نویسنده

  • Mehdi Hassani Department of Mathematics, University of Zanjan University Blvd., 45371-38791, Zanjan.
چکیده مقاله:

The asymptotic behaviour of the sequence with general term $P_n=(varphi(1)+varphi(2)+cdots+varphi(n))/(1+2+cdots+n)$, is studied which appears in the studying of coprime integers, and an explicit bound for the difference $P_n-6/pi^2$ is found.

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

on a sequence related to the coprime integers

the asymptotic behaviour of the sequence with general term $p_n=(varphi(1)+varphi(2)+cdots+varphi(n))/(1+2+cdots+n)$, is studied which appears in the studying of coprime integers, and an explicit bound for the difference $p_n-6/pi^2$ is found.

متن کامل

On exponentially coprime integers

d|en d denote the number and the sum of exponential divisors of n, respectively. Properties of these functions were investigated by several authors, see [1], [2], [3], [5], [6], [8]. Two integers n,m > 1 have common exponential divisors iff they have the same prime factors and for n = ∏r i=1 p ai i , m = ∏r i=1 p bi i , ai, bi ≥ 1 (1 ≤ i ≤ r), the greatest common exponential divisor of n and m is

متن کامل

On Using (z2,+) Homomorphisms to Generate Pairs of Coprime Integers

A. We use the group (Z2,+) and two associated homomorphisms, τ0, τ1, to generate all distinct, non-zero pairs of coprime, positive integers which we describe within the context of a binary tree which we denote T . While this idea is related to the Stern-Brocot tree and the map of relatively prime pairs, the parents of an integer pair these trees do not necessarily correspond to the paren...

متن کامل

On Using (z2,+) Automorphisms to Generate Pairs of Coprime Integers

A. We use the group (Z2,+) and two associated automorphisms, τ0, τ1, to generate all distinct, non-zero pairs of coprime, positive integers which we describe within the context of a binary tree which we denote T . While this idea is related to the Stern-Brocot tree and the map of relatively prime pairs, the parents of an integer pair these trees do not necessarily correspond to the paren...

متن کامل

Inhomogeneous approximation by coprime integers

This paper addresses a problem recently raised by Laurent and Nogueira about inhomogeneous Diophantine approximation with coprime integers. A corollary of our main theorem is that for any irrational α ∈ R and for any γ ∈ R and > 0 there are infinitely many pairs of coprime integers m,n such that |nα−m− γ| ≤ 1/|n| . This improves upon previously known results, in which the exponent of approximat...

متن کامل

On the Kernel of the Coprime Graph of Integers

Abstract Let (V,E) be the coprime graph with vertex set V = {1, 2, . . . , n} and edges (i, j) ∈ E if gcd(i, j) = 1. We determine the kernels of the coprime graph and its loopless counterpart as well as so-called simple bases for them (in case such bases exist), which means that basis vectors have entries only from {−1, 0, 1}. For the loopless version knowledge about the value distribution of M...

متن کامل

منابع من

با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ذخیره در منابع من قبلا به منابع من ذحیره شده

{@ msg_add @}


عنوان ژورنال

دوره 01  شماره 2

صفحات  31- 37

تاریخ انتشار 2014-12-01

با دنبال کردن یک ژورنال هنگامی که شماره جدید این ژورنال منتشر می شود به شما از طریق ایمیل اطلاع داده می شود.

میزبانی شده توسط پلتفرم ابری doprax.com

copyright © 2015-2023