**Volume 28** ▶ Number 1 ▷ Number 2 ▷ Number 3 ▷ Number 4 (Online First)

- Volume opened: 12 October 2022
- Status: In progress

**On recurrence results from matrix transforms**

*Original research paper. Pages 589—592*

Ömür Deveci and Anthony G. Shannon

Download PDF (693 Kb) | Abstract

**On a new class of the generalized Gauss k-Pell numbers and their polynomials**

*Original research paper. Pages 593—602*

Ahmet Kaya and Hayrullah Özimamoğlu

Download PDF (174 Kb) | Abstract

*k*-Pell numbers. There are relationships discovered between the class of generalized Gauss

*k*-Pell numbers and the typical Gauss Pell numbers. Also, we generalize the known Gauss Pell polynomials, and call such polynomials as the generalized Gauss

*k*-Pell polynomials. We obtain relations between the class of the generalized Gauss

*k*-Pell polynomials and the typical Gauss Pell polynomials. Furthermore, we provide matrices for the novel generalizations of these numbers and polynomials. After that, we obtain Cassini’s identities for these numbers and polynomials.

**Some multiple Dirichlet series of completely multiplicative arithmetic functions**

*Original research paper. Pages 603—616*

Nabil Tahmi and Abdallah Derbal

Download PDF (216 Kb) | Abstract

where and is a completely multiplicative or a specially multiplicative arithmetic function of a single variable. We obtain formulas for these series expressed by infinite products over the primes. We also consider the cases of certain particular completely multiplicative and specially multiplicative functions.

**Asymptotics of sums of divisor functions over sequences with restricted factorization structure**

*Original research paper. Pages 617—634*

Rafael Jakimczuk and Matilde Lalín

Download PDF (235 Kb) | Abstract

*h*-free numbers,

*h*-full numbers and other arithmetically interesting sets and conditions. The main tool for obtaining these results is Perron’s formula.

**Hook type tableaux and partition identities**

*Original research paper. Pages 635—647*

Koustav Banerjee and Manosij Ghosh Dastidar

Download PDF (205 Kb) | Abstract

**Asymptotic formula of a “hyperbolic” summation related to the Piltz divisor function**

*Original research paper. Pages 648—655*

Mihoub Bouderbala and Meselem Karras

Download PDF (216 Kb) | Abstract

such that , where denotes the Piltz divisor function, and is the unitary analogue function of .

**Arithmetical functions associated with conjugate pairs of sets under regular convolutions**

*Original research paper. Pages 656—665*

Pentti Haukkanen

Download PDF (179 Kb) | Abstract

*P*and

*Q*of the set of positive integers is said to form a conjugate pair if each positive integer

*n*possesses a unique factorization of the form

*n*=

*ab*,

*a*∈

*P*,

*b*∈

*Q*. In this paper we generalize conjugate pairs of sets to the setting of regular convolutions and study associated arithmetical functions. Particular attention is paid to arithmetical functions associated with

*k*-free integers and

*k*-th powers under regular convolution.

**New type degenerate Stirling numbers and Bell polynomials**

*Original research paper. Pages 666—676*

Hye Kyung Kim

Download PDF (185 Kb) | Abstract

**Equations of two sets of consecutive square sums**

*Original research paper. Pages 677—691*

P. J. Bush and K. V. Murphy

Download PDF (186 Kb) | Abstract

**On a generalization of a function of J. Sándor**

*Original research paper. Pages 692—697*

V. Siva Rama Prasad and P. Anantha Reddy

Download PDF (198 Kb) | Abstract

**Linear mappings in paraletrix spaces and their application to fractional calculus**

*Original research paper. Pages 698—709*

R. U. Ndubuisi, U. K. Nwajeri, C. P. Onyenegecha, K. M. Patil, O. G. Udoaka and W. I. Osuji

Download PDF (549 Kb) | Abstract

**On Vandiver’s arithmetical function – II**

*Original research paper. Pages 710—718*

József Sándor

Download PDF (201 Kb) | Abstract

introduced in [2].

**Congruences via umbral calculus**

*Original research paper. Pages 719—729*

Abdelkader Benyattou

Download PDF (193 Kb) | Abstract

**Counting general power residues**

*Original research paper. Pages 730—743*

Samer Seraj

Download PDF (197 Kb) | Abstract

*k*≥ 2 and the remainders of these powers upon division by a fixed integer

*n*≥ 2 are found. It is natural to ask how many distinct remainders are produced. By building on the work of Stangl, who published the

*k*= 2 case in Mathematics Magazine in 1996, we find essentially closed formulas that allow for the computation of this number for any

*k*. Along the way, we provide an exposition of classical results on the multiplicativity of this counting function and results on the number of remainders that are coprime to the modulus

*n*.

**Explicit formulas for sums related to Dirichlet L-functions**

*Original research paper. Pages 744—748*

Brahim Mittou

Download PDF (182 Kb) | Abstract

are given in this paper by using the properties of character sums and Bernoulli polynomials.

**The integrality of the Genocchi numbers obtained through a new identity and other results**

*Original research paper. Pages 749—757*

Bakir Farhi

Download PDF (199 Kb) | Abstract

**On combined 3-Fibonacci sequences**

*Original research paper. Pages 758—764*

Krassimir T. Atanassov, Lilija C. Atanassova and Anthony G. Shannon

Download PDF (145 Kb) | Abstract

A secondary goal of the paper is to put the disarray of this part of number theory into some semblance of order with a selection of representative references. This gives rise to a ‘combobulated sequence’, so-called because it restores partial order to a disarray of many papers into three classes, which are fuzzy in both their membership and non-membership because of their diverse and non-systematic derivations.

*This volume of the International Journal “Notes on Number Theory and Discrete Mathematics” is published with the financial support of the Bulgarian National Science Fund, Grant Ref. No. KP-06-NP3/43/2021.*