Results 21 to 30 of about 654 (59)
Mathematics of Computation, 2013 Here, we give an algorithm to detect all perfect repdigits in any base g > 1. As an application, we find all such examples when g ∈ [2, . . . , 333], extending a calculation from [2].
K. Broughan +2 more
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Harmonic numbers, harmonic series and zeta function
Moroccan Journal of Pure and Applied Analysis, 2018 This paper reviews, from different points of view, results on Bernoulli numbers and polynomials, the distribution of prime numbers in connexion with the Riemann hypothesis. We give an account on the theorem of G. Robin, as formulated by J. Lagarias.
Sebbar Ahmed
doaj +1 more source
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
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The sharp version of a strongly starlikeness condition
Acta Universitatis Sapientiae: Mathematica, 2017 In this paper we give the best form of a strongly starlikeness condition. Some consequences of this result are deduced. The basic tool of the research is the method of differential subordinations.
Engel Olga, Juma Abdul Rahman S.
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The average order of the Dirichlet series of the gcd-sum function [PDF]
, 2007 Using a result of Bordellès, we derive the second term and improved error expressions for the partial sums of the Dirichlet series of the gcd-sum function, for all real values of the ...
Broughan, Kevin A.
core
Averages of Ramanujan sums: Note on two papers by E. Alkan
, 2014 We give a simple proof and a multivariable generalization of an identity due to E. Alkan concerning a weighted average of the Ramanujan sums. We deduce identities for other weighted averages of the Ramanujan sums with weights concerning logarithms ...
Tóth, László
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, 2012 In the study of the 2-adic sum of digits function S2(n), the arithmetical function u(0) = 0 and u(n) = (−1)n−1 for n ≥ 1 plays a very important role. In this paper, we firstly generalize the relation between S2(n) and u(n) to a bijective relation between
Y. Kamiya, L. Murata
semanticscholar +1 more source
Remarks on the number of prime divisors of integers
, 2013 In this paper, we obtain explicit bounds for sums ∑k n ω(k) and ∑k n Ω(k)−ω(k) , where ω(k) denotes the number of distinct prime divisors of k , and Ω(k) denotes the total number of its prime divisors.
M. Hassani
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Note on the number of divisors of reducible quadratic polynomials
, 2018 In a recent paper, Lapkova uses a Tauberian theorem to derive the asymptotic formula for the divisor sum $\sum_{n \leq x} d( n (n+v))$ where $v$ is a fixed integer and $d(n)$ denotes the number of divisors of $n$.
Dudek, Adrian W. +2 more
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, 2013 We prove that there are no integers n 2 and k 2 such that n divides W(nk) sk(n). For k 2 this settles a conjecture of Adiga and Ramaswamy. MATHEMATICS SUBJECT CLASSIFICATION (2010). 11A25.
H. Alzer, J. Sándor
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