Results 21 to 30 of about 595 (44)

A generalization of Menon's identity with Dirichlet characters

, 2018
The classical Menon's identity [7] states that \begin{equation*}\label{oldbegin1} \sum_{\substack{a\in\Bbb Z_n^\ast }}\gcd(a -1,n)=\varphi(n) \sigma_{0} (n), \end{equation*} where for a positive integer $n$, $\Bbb Z_n^\ast$ is the group of units of the
Hu, Xiaoyu, Kim, Daeyeoul, Li, Yan
core   +1 more source

Binomial convolution sum of divisor functions associated with Dirichlet character modulo 8

Open Mathematics
In this article, we compute binomial convolution sums of divisor functions associated with the Dirichlet character modulo 8, which is the remaining primitive Dirichlet character modulo powers of 2 yet to be considered.
Jin Seokho, Park Ho
doaj   +1 more source

On the proximity of large primes

, 2017
By a sphere-packing argument, we show that there are infinitely many pairs of primes that are close to each other for some metrics on the integers. In particular, for any numeration basis $q$, we show that there are infinitely many pairs of primes the ...
Luca, Florian, Shi, Minjia, Solé, Patrick   +2 more
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Note on sums involving the Euler function

, 2018
In this note, we provide refined estimates of the following sums involving the Euler totient function: $$\sum_{n\le x} \phi\left(\left[\frac{x}{n}\right]\right) \qquad \text{and} \qquad \sum_{n\le x} \frac{\phi([x/n])}{[x/n]}$$ where $[x]$ denotes the ...
Chern, Shane
core   +1 more source

An identity for a class of arithmetical functions of several variables

, 1993
International Journal of Mathematics and Mathematical Sciences, Volume 16, Issue 2, Page 355-358, 1993.
Pentti Haukkanen
wiley   +1 more source

Dirichlet summations and products over primes

, 1991
International Journal of Mathematics and Mathematical Sciences, Volume 16, Issue 2, Page 359-372, 1993.
Geoffrey B. Campbell
wiley   +1 more source

Arithmetic functions associated with infinitary divisors of an integer

, 1993
International Journal of Mathematics and Mathematical Sciences, Volume 16, Issue 2, Page 373-383, 1993.
Graeme L. Cohen, Peter Hagis
wiley   +1 more source

A note on Deaconescu’s conjecture

Annals of the West University of Timisoara: Mathematics and Computer Science
Hasanalizade [5] studied Deaconescu’s conjecture for positive composite integer n. A positive composite integer n ≥ 4 is said to be a Deaconescu number if S2(n) | ϕ(n) − 1.
Mandal Sagar
doaj   +1 more source

Extreme values of the Dedekind $\Psi$ function

, 2011
Let $\Psi(n):=n\prod_{p | n}(1+\frac{1}{p})$ denote the Dedekind $\Psi$ function. Define, for $n\ge 3,$ the ratio $R(n):=\frac{\Psi(n)}{n\log\log n}.$ We prove unconditionally that $R(n)< e^\gamma$ for $n\ge 31.$ Let $N_n=2...p_n$ be the primorial of ...
Planat, Michel, Solé, Patrick
core   +1 more source

Middle divisors and $\sigma$-palindromic Dyck words

, 2017
Given a real number $\lambda > 1$, we say that $d|n$ is a $\lambda$-middle divisor of $n$ if $$ \sqrt{\frac{n}{\lambda}} < d \leq \sqrt{\lambda n}. $$ We will prove that there are integers having an arbitrarily large number of $\lambda$-middle divisors ...
Caballero, José Manuel Rodríguez
core