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On an additive arithmetic function [PDF]

open access: greenPacific Journal of Mathematics, 1977
Let \(n\) be a positive integer, \(n=\prod\limits_{i=1}^rp_i^{\alpha_i}\) in canonical form, and let \(A(n)=\sum\limits_{i=1}^r\alpha_ip_i\). Clearly \(A\) is an additive arithmetic function.
Krishnaswami Alladi, P. Erdős
openalex   +5 more sources

An arithmetic function [PDF]

open access: goldBulletin of the American Mathematical Society, 1937
L. Carlitz
openalex   +4 more sources

A simple proof of generalizations of number-theoretic sums [PDF]

open access: yesSongklanakarin Journal of Science and Technology (SJST), 2022
For positive integers 𝑘, 𝑚, and 𝑛, let 𝑆𝑘 𝑚(𝑛) be the sum of all elements in the finite set {𝑥 𝑘 : 1 ≤ 𝑥 ≤ 𝑛⁄𝑚 , (𝑥, 𝑛) = 1}. The formula for 𝑆𝑘 𝑚(𝑛) is established and simpler formulae for 𝑆𝑘 𝑚(𝑛) under some conditions on 𝑚 and 𝑛 are verified. The
Yanapat Tongron   +1 more
doaj   +1 more source

Density of Arithmetic Representations of Function Fields [PDF]

open access: yesÉpijournal de Géométrie Algébrique, 2022
We propose a conjecture on the density of arithmetic points in the deformation space of representations of the \'etale fundamental group in positive characteristic. This?
Hélène Esnault, Moritz Kerz
doaj   +1 more source

ON A SUM INVOLVING CERTAIN ARITHMETIC FUNCTIONS ON PIATETSKI–SHAPIRO AND BEATTY SEQUENCES

open access: yesПроблемы анализа, 2022
Let 𝑐, 𝛼, 𝛽 ∈ R be such that ...
T. Srichan
doaj   +1 more source

Math Can Be Visual—Teaching and Understanding Arithmetical Functions through Visualization

open access: yesMathematics, 2022
Number theory is an area of mathematics not unknown to students majoring in mathematics teaching. As early as in junior high, they may encounter basic number theory concepts such as prime numbers, multiples, divisors, or even the fundamental theorem of ...
Szilárd Svitek   +2 more
doaj   +1 more source

The local limit theorem of Delange in the Knopfmacher's semigroup

open access: yesLietuvos Matematikos Rinkinys, 2004
An asymptotic formula of the mean value of multiplicative arithmetic function from the class Ma(G)  with asymptotical expansion of the main term is obtained. In the present paper the local limit theorem of the H. Delange type is proved.
Rimantas Skrabutėnas
doaj   +3 more sources

Asymptotical expansions in the Kubilius theorem of large deviations

open access: yesLietuvos Matematikos Rinkinys, 2005
In the present paper, a local theorem of large deviations for arithmetic functions defined in Knopfmacher’s semigroup is obtained.
Rimantas Skrabutėnas
doaj   +3 more sources

New Arithmetic Operations of Non-Normal Fuzzy Sets Using Compatibility

open access: yesAxioms, 2023
The new arithmetic operations of non-normal fuzzy sets are studied in this paper by using the extension principle and considering the general aggregation function. Usually, the aggregation functions are taken to be the minimum function or t-norms.
Hsien-Chung Wu
doaj   +1 more source

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