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A characterization of some q-multiplicative functions

Jean-Loup Mauclaire (2005)

Acta Arithmetica

A class of weakly perfect graphs

H. R. Maimani, M. R. Pournaki, S. Yassemi (2010)

Czechoslovak Mathematical Journal

A graph is called weakly perfect if its chromatic number equals its clique number. In this note a new class of weakly perfect graphs is presented and an explicit formula for the chromatic number of such graphs is given.

A convolution theorem with applications to some divisor functions.

A. Ivic (1978)

Publications de l'Institut Mathématique [Elektronische Ressource]

A formula for the number of solutions of a restricted linear congruence

K. Vishnu Namboothiri (2021)

Mathematica Bohemica

Consider the linear congruence equation $x_{1} + ... + x_{k} \equiv b (mod n^{s})$ for $b \in ℤ$ , $n, s \in ℕ$ . Let ${(a, b)}_{s}$ denote the generalized gcd of $a$ and $b$ which is the largest $l^{s}$ with $l \in ℕ$ dividing $a$ and $b$ simultaneously. Let $d_{1}, ..., d_{τ (n)}$ be all positive divisors of $n$ . For each $d_{j} ∣ n$ , define $𝒞_{j, s} (n) = {1 \leq x \leq n^{s} : {(x, n^{s})}_{s} = d_{j}^{s}}$ . K. Bibak et al. (2016) gave a formula using Ramanujan sums for the number of solutions of the above congruence equation with some gcd restrictions on $x_{i}$ . We generalize their result with generalized gcd restrictions on $x_{i}$ and prove that for the above linear congruence, the number of solutions...

A generalization of Menon's identity with respect to a set of polynomials.

Haukkanen, P., Wang, J. (1996)

Portugaliae Mathematica

A generalization of Pillai's arithmetical function involving regular convolutions

László Tóth (1998)

Acta Mathematica et Informatica Universitatis Ostraviensis

A generalization of the Smarandache function to several variables.

Hungerbühler, Norbert, Specker, Ernst (2006)

Integers

A generalization of the Subbarao identity.

Penntti Haukkanen (1988)

Aequationes mathematicae

A matrix inequality for Möbius functions.

Bordellès, Olivier, Cloitre, Benoit (2009)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

A Menon-type identity using Klee's function

Arya Chandran, Neha Elizabeth Thomas, K. Vishnu Namboothiri (2022)

Czechoslovak Mathematical Journal

Menon’s identity is a classical identity involving gcd sums and the Euler totient function $φ$ . A natural generalization of $φ$ is the Klee’s function $Φ_{s}$ . We derive a Menon-type identity using Klee’s function and a generalization of the gcd function. This identity generalizes an identity given by Y. Li and D. Kim (2017).

A million new amicable pairs.

Garcia, Mariano (2001)

Journal of Integer Sequences [electronic only]

A multivariate arithmetic function of combinatorial and topological significance.

Liskovets, Valery A. (2010)

Integers

A new kind of Diophantine equations

Binzhou Xia, Tianxin Cai (2011)

Acta Arithmetica

A note on $(a, b)$ -Fibonacci sequences and specially multiplicative arithmetic functions

Emil Daniel Schwab, Gabriela Schwab (2024)

Mathematica Bohemica

A specially multiplicative arithmetic function is the Dirichlet convolution of two completely multiplicative arithmetic functions. The aim of this paper is to prove explicitly that two mathematical objects, namely $(a, b)$ -Fibonacci sequences and specially multiplicative prime-independent arithmetic functions, are equivalent in the sense that each can be reconstructed from the other. Replacing one with another, the exploration space of both mathematical objects expands significantly.

Currently displaying 1 – 20 of 487