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On Certain Arithmetic Functions [PDF]

, 2000
In the recent book there appear certain arithmetic functions which are similar to the Smarandache function. In a recent paper we have considered certain generalization or duals of the Smarandache function. In this note we wish to point out that the arithmetic functions introduced all are particular cases of our function Fj, defined in the following ...
Sandor, J.
openaire   +3 more sources

Inequalities with Some Arithmetic Functions

Mathematics
In the paper, some new inequalities are formulated and proved with the classical arithmetic functions φ (of Euler) and ψ (of Dedekind).
József Sándor, Krassimir Atanassov
doaj   +2 more sources

Functions Definable by Arithmetic Circuits [PDF]

, 2009
An arithmetic circuit is a labelled, directed, acyclic graph specifying a cascade of arithmetic and logical operations to be performed on sets of non-negative integers. In this paper, we consider the definability of functions from tuples of sets of non-negative integers to sets of non-negative integers by means of arithmetic circuits.
Ian Pratt-Hartmann, Ivo Düntsch
openaire   +2 more sources

The fractional sum of small arithmetic functions [PDF]

Journal of Number Theory, 2021
where f is an arithmetic function and ⌊·⌋ denotes the greatest integer function. When f(n) = n, this is the classic Dirichlet divisor problem. Such sums do not seem to have a name in the literature yet, so we propose to call Sf the “fractional sum of f .”
Joshua Stucky
semanticscholar   +1 more source

Independence measures of arithmetic functions

, 2011
The notion of algebraic dependence in the ring of arithmetic functions with addition and Dirichlet product is considered. Measures for algebraic independence are derived.
T. Komatsu, V. Laohakosol, Pattira Ruengsinsub   +2 more
semanticscholar   +2 more sources

On certain equations and inequalities involving the arithmetical functions φ(n) and d(n) – II [PDF]

Notes on Number Theory and Discrete Mathematics, 2023
In papers [3] and [5] we have studied certain equations and inequalities involving the arithmetical functions φ(n) and d(n). In this paper we will consider some other equations. Some open problems will be stated, too.
József Sándor
doaj   +1 more source

Polynomial Expressions for Certain Arithmetic Functions

Journal of Mountain Research, 2023
t: We exhibit polynomial expressions for the arithmetic functions and , the number of representations of n as a sum of k squares and k triangular numbers, respectively, and also for the color ...
M. Pathan, M. M. Iddrisu, J. López-Bonilla, H. Kumar   +3 more
semanticscholar   +1 more source

An Optoelectronic Resistive Switching Memory with Integrated Demodulating and Arithmetic Functions

Advanced Materials, 2015
Xiaojian Zhu, Huali Yang, Xinxin Chen
exaly   +2 more sources

Some Properties of Euler’s Function and of the Function τ and Their Generalizations in Algebraic Number Fields

Mathematics, 2021
In this paper, we find some inequalities which involve Euler’s function, extended Euler’s function, the function τ, and the generalized function τ in algebraic number fields.
Nicuşor Minculete, Diana Savin
doaj   +1 more source

CLASSIFICATION ON ARITHMETIC FUNCTIONS AND CORRESPONDING FREE-MOMENT L-FUNCTIONS

Bulletin of the Korean Mathematical Society, 2015
Ilwoo Cho, Cho Ilwoo
exaly   +2 more sources