Results 21 to 30 of about 85,514 (301)
New properties of arithmetic functions related to gcd and lcm [PDF]
Notes on Number Theory and Discrete MathematicsThis paper explores additional properties of the arithmetic functions f_α(n) and g_α(n), defined respectively by f_α(n)=Πʳᵢ₌₁pᵢ^{(eᵢ,α)} and g_α(n)=Πʳᵢ₌₁pᵢ^{[eᵢ,α]}, where n=Πʳᵢ₌₁pᵢ^eᵢ is the prime factorization of a positive integer n>1, (a,b) and [a,b]
Brahim Mittou
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Characterizations of L-additive functions via generalized arithmetic convolutions [PDF]
Notes on Number Theory and Discrete MathematicsThis paper investigates the properties of L-additive functions within the algebraic frameworks of two generalized arithmetic convolutions: the K-convolution and Narkiewicz's A-convolution.
Champak Talukdar +2 more
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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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Multidimensional local theorem in the Knopfmachers semigroup
Lietuvos Matematikos Rinkinys, 2007 In the presentpaper a multidimensionallocal theorem for arithmetic functions definedin the Knopfmachers semigroup G is obtained.
Rimantas Skrabutėnas
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An identity involving the function ep(n) [PDF]
, 2007 The main purpose of this paper is to study the relationship between the Riemann zeta-function and an infinite series involving the Smarandache function ep(n) by using the elementary method, and give an interesting ...
Xiaowei, Pan, Zhang, Pei
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Divisibility of arithmetic functions [PDF]
Pacific Journal of Mathematics, 1984 A derivative-like operator on the Dirichlet ring of arithmetic functions is used to develop formulas for the greatest common divisor of certain arithmetic functions. It is conjectured that formulas of this type hold more generally.
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The mean value of the function d(n)/d*(n) in arithmetic progressions [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 Let d(n) and d*(n) be, respectively, the number of divisors and the number of unitary divisors of an integer n≥1. A divisor d of an integer is to be said unitary if it is prime over n/d.
Ouarda Bouakkaz, Abdallah Derbal
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A Functional Equation in Arithmetic [PDF]
Transactions of the American Mathematical Society, 1936 which occurs in all theories of numerical functions hitherto considered. The two most highly developed theories of this kind are those in which multiplication in the ring of all numerical functions is abstractly identical with C (Cauchy) or D (Dirichlet) multiplication of infinite series.t Lehmer's five postulates are sufficient for the development of ...
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Representation zeta functions of compact p-adic analytic groups and arithmetic groups [PDF]
, 2013 We introduce new methods from p-adic integration into the study of representation zeta functions associated to compact p-adic analytic groups and arithmetic groups.
Onn, Uri +3 more
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Sequences in finite fields yielding divisors of Mersenne, Fermat and Lehmer numbers, II [PDF]
Notes on Number Theory and Discrete MathematicsLet ρ be an odd prime ≥ 11. In Part I, starting from an M-cycle in a finite field 𝔽_ρ, we have established how the divisors of Mersenne, Fermat and Lehmer numbers arise.
A. M. S. Ramasamy
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