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Two arithmetic functions related to Euler's and Dedekind's functions [PDF]
Notes on Number Theory and Discrete MathematicsTwo new arithmetic functions are introduced. In some sense, they are modifications of Euler's and Dedekind's functions. Some properties of the new functions are studied.
Krassimir Atanassov
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A note on newly introduced arithmetic functions φ+ and σ+ [PDF]
Notes on Number Theory and Discrete MathematicsIn a recent paper [7], the authors introduced new arithmetic functions φ⁺, σ⁺ related to the classical functions φ, and σ, respectively. In this note, we study the behavior of Σ_{n≤x, ω(n)=2}(φ⁺-φ)(n), and Σ_{n≤x, ω(n)=2}(σ⁺-σ)(n), for any real number x ...
Sagar Mandal
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Arithmetic in the developing brain: A review of brain imaging studies
Developmental Cognitive Neuroscience, 2018 Brain imaging studies on academic achievement offer an exciting window on experience-dependent cortical plasticity, as they allow us to understand how developing brains change when children acquire culturally transmitted skills. This contribution focuses
Lien Peters, Bert De Smedt
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Objects generated by an arbitrary natural number. Part 4: New aspects [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 The set Set(n), generated by an arbitrary natural number n, was defined in [3]. There, and in [5, 6], some arithmetic functions and arithmetic operators of a modal and topological types are defined over the elements of Set(n).
Krassimir Atanassov
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Objects generated by an arbitrary natural number. Part 3: Standard modal-topological aspect [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 The set Set(n), generated by an arbitrary natural number n, was defined in [3]. There, and in [4], some arithmetic functions and arithmetic operators of a modal type are defined over the elements of Set(n).
Krassimir Atanassov
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On a modification of Set(n) [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 A modification of the set Set(n) for a fixed natural number n is introduced in the form: Set(n, f), where f is an arithmetic function. The sets Set(n,φ), Set(n,ψ), Set(n,σ) are discussed, where φ, ψ and σ are Euler's function, Dedekind's function and the
Krassimir T. Atanassov, József Sándor
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On certain arithmetical functions of exponents in the factorization of integers [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 Some new results for the maximum and minimum exponents in factorizing integers are obtained. Related functions and generalized arithmetical functions are also introduced.
József Sándor, Krassimir T. Atanassov
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A simple proof of generalizations of number-theoretic sums [PDF]
Songklanakarin 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
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Math Can Be Visual—Teaching and Understanding Arithmetical Functions through Visualization
Mathematics, 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
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Density of Arithmetic Representations of Function Fields [PDF]
Épijournal 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
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