**Volume 29** ▶ Number 1 ▷ Number 2 ▷ Number 3 ▷ Number 4 (Online First)

**Pauli–Leonardo quaternions**

*Original research paper. Pages 1—16*

Zehra İşbilir, Mahmut Akyiğit and Murat Tosun

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**On distribution of the number of semisimple rings of order at most x in an arithmetic progression**

*Original research paper. Pages 17—23*

Thorranin Thansri, Teerapat Srichan and Pinthira Tangsupphathawat

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where denotes the number of non-isomorphic finite semisimple rings with elements.

**A note on the number a^{n}+ b^{n} – dc^{n}**

*Original research paper. Pages 24—29*

Nguyen Viet Dung and Luu Ba Thang

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**Two generalizations of Liouville λ function**

*Original research paper. Pages 30—39*

André Pierro de Camargo

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**A study of the complexification process of the ( s,t)-Perrin sequence**

*Original research paper. Pages 40—47*

Renata Passos Machado Vieira, Francisco Regis Vieira Alves and Paula Maria Machado Cruz Catarino

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*s*,

*t*)-Perrin sequence in its complex process. Thus, from the one-dimensional model of the generalized (

*s*,

*t*)-Perrin sequence, imaginary units are inserted, starting with the insertion of unit

*i*, called two-dimensional relations. Altogether, we have the

*n*-dimensional relationships of the generalized (

*s*,

*t*)-Perrin sequence.

**Transcendental properties of the certain mix infinite products**

*Original research paper. Pages 48—61*

Eiji Miyanohara

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In this paper, we prove that the infinite product with is either rational or transcendental. Moreover, we give sufficient conditions that is transcendental.

**A primality test for Kp^{n} + 1 numbers and a generalization of Safe primes and Sophie Germain primes**

*Original research paper. Pages 62—77*

Abdelrahman Ramzy

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**Sums involving the binomial coefficients, Bernoulli numbers of the second kind and harmonic numbers**

*Original research paper. Pages 78—97*

Necdet Batır and Anthony Sofo

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and

where are Bernoulli numbers of the second kind, and is the Riemann zeta function. We also give an alternate proof of the series representations for the constants and given by Blagouchine and Coppo.

**A generalized computation procedure for Ramanujan-type identities and cubic Shevelev sum**

*Original research paper. Pages 98—129*

Peter J.-S. Shiue, Anthony G. Shannon, Shen C. Huang, Jorge E. Reyes

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

*Original research paper. Pages 130—136*

József Sándor

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**Congruences for harmonic sums**

*Original research paper. Pages 137—146*

Yining Yang and Peng Yang

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to supercongruences modulo and for odd and even where prime and .

**A note on edge irregularity strength of firefly graph**

*Original research paper. Pages 147—153*

Umme Salma, H. M. Nagesh and D. Prahlad

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**Hybrid hyper-Fibonacci and hyper-Lucas numbers**

*Original research paper. Pages 154—170*

Yasemin Alp

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**Objects generated by an arbitrary natural number. Part 3: Standard modal-topological aspect**

*Original research paper. Pages 171—180*

Krassimir Atanassov

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**Corrigendum to: “Some modular considerations regarding odd perfect numbers – Part II” [Notes on Number Theory and Discrete Mathematics, 2020, Vol. 26, No. 3, 8–24]**

*Corrigendum. Pages 181—184*

Jose Arnaldo Bebita Dris and Immanuel Tobias San Diego

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*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-NP4/30/2022.*

**Volume 29** ▶ Number 1 ▷ Number 2 ▷ Number 3 ▷ Number 4 (Online First)