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Acta Arithmetica

### A class of weakly perfect graphs

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.

Publications de l'Institut Mathématique [Elektronische Ressource]

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

Mathematica Bohemica

Consider the linear congruence equation ${x}_{1}+...+{x}_{k}\equiv b\phantom{\rule{4.44443pt}{0ex}}\left(mod\phantom{\rule{0.277778em}{0ex}}{n}^{s}\right)$ for $b\in ℤ$, $n,s\in ℕ$. Let ${\left(a,b\right)}_{s}$ denote the generalized gcd of $a$ and $b$ which is the largest ${l}^{s}$ with $l\in ℕ$ dividing $a$ and $b$ simultaneously. Let ${d}_{1},...,{d}_{\tau \left(n\right)}$ be all positive divisors of $n$. For each ${d}_{j}\mid n$, define ${𝒞}_{j,s}\left(n\right)=\left\{1\le x\le {n}^{s}:{\left(x,{n}^{s}\right)}_{s}={d}_{j}^{s}\right\}$. 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.

Portugaliae Mathematica

### A generalization of Pillai's arithmetical function involving regular convolutions

Acta Mathematica et Informatica Universitatis Ostraviensis

Integers

### A generalization of the Subbarao identity.

Aequationes mathematicae

### A matrix inequality for Möbius functions.

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

### A Menon-type identity using Klee's function

Czechoslovak Mathematical Journal

Menon’s identity is a classical identity involving gcd sums and the Euler totient function $\phi$. A natural generalization of $\phi$ is the Klee’s function ${\Phi }_{s}$. 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.

Journal of Integer Sequences [electronic only]

Integers

Acta Arithmetica

Integers

### A note on generalized mobius ...-functions

Revista colombiana de matematicas

### A note on multiplicatively e-perfect numbers.

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

### A note on perfect totient numbers.

Journal of Integer Sequences [electronic only]

### A note on primes p with $\sigma \left({p}^{m}\right)={z}^{n}$

Colloquium Mathematicae

Acta Arithmetica

### A note on Sándor type functions.

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

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