On a sequence related to the coprime integers
author
Abstract:
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.
similar resources
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.
full textOn 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
full textOn 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...
full textOn 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...
full textInhomogeneous 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...
full textOn 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...
full textMy Resources
Journal title
volume 01 issue 2
pages 31- 37
publication date 2014-12-01
By following a journal you will be notified via email when a new issue of this journal is published.
Hosted on Doprax cloud platform doprax.com
copyright © 2015-2023