Results 1 to 10 of about 34 (34)

Arithmetic convolution sums derived from eta quotients related to divisors of 6

Open Mathematics, 2022
The aim of this paper is to find arithmetic convolution sums of some restricted divisor functions. When divisors of a certain natural number satisfy a suitable condition for modulo 12, those restricted divisor functions are expressed by the coefficients ...
Ikikardes Nazli Yildiz, Hwang Jihyun, Kim Daeyeoul   +2 more
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The multinomial convolution sum of a generalized divisor function

Open Mathematics, 2022
The main theorem of this article is to evaluate and express the multinomial convolution sum of the divisor function σr♯(n;N/4,N){\sigma }_{r}^{\sharp }\left(n;\hspace{0.33em}N\hspace{-0.08em}\text{/}\hspace{-0.08em}4,N) in as a simple form as possible ...
Park Ho
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Identities Arising from Binomial-Like Formulas Involving Divisors of Numbers

Annales Mathematicae Silesianae, 2023
In this article, we derive a great number of identities involving the ω function counting distinct prime divisors of a given number n. These identities also include Pochhammer symbols, Fibonacci and Lucas numbers and many more.
Gryszka Karol
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Evaluation of the convolution sum involving the sum of divisors function for 22, 44 and 52

Open Mathematics, 2017
The convolution sum, ∑(l,m)∈N02αl+βm=nσ(l)σ(m), $ \begin{array}{} \sum\limits_{{(l\, ,m)\in \mathbb{N}_{0}^{2}}\atop{\alpha \,l+\beta\, m=n}} \sigma(l)\sigma(m), \end{array} $ where αβ = 22, 44, 52, is evaluated for all natural numbers n. Modular forms
Ntienjem Ebénézer
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Evaluation of the convolution sums ∑al+bm=n lσ(l) σ(m) with ab ≤ 9

Open Mathematics, 2017
The generating functions of divisor functions are quasimodular forms of weight 2 and their products belong to a space of quasimodular forms of higher weight.
Park Yoon Kyung
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Harmonic numbers, harmonic series and zeta function

Moroccan Journal of Pure and Applied Analysis, 2018
This paper reviews, from different points of view, results on Bernoulli numbers and polynomials, the distribution of prime numbers in connexion with the Riemann hypothesis. We give an account on the theorem of G. Robin, as formulated by J. Lagarias.
Sebbar Ahmed
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On characterizing potential friends of 20

Annals of the West University of Timisoara: Mathematics and Computer Science
Does 20 have a friend? Or is it a solitary number? A folklore conjecture asserts that 20 has no friends, i.e., it is a solitary number. In this article, we prove that a friend N of 20 is of the form N = 2 · 52a ·m2, with (3;m) = (7;m) = 1 and it has at ...
Chatterjee Tapas, Mandal Sagar, Mandal Sourav   +2 more
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Binomial convolution sum of divisor functions associated with Dirichlet character modulo 8

Open Mathematics
In this article, we compute binomial convolution sums of divisor functions associated with the Dirichlet character modulo 8, which is the remaining primitive Dirichlet character modulo powers of 2 yet to be considered.
Jin Seokho, Park Ho
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A note on Deaconescu’s conjecture

Annals of the West University of Timisoara: Mathematics and Computer Science
Hasanalizade [5] studied Deaconescu’s conjecture for positive composite integer n. A positive composite integer n ≥ 4 is said to be a Deaconescu number if S2(n) | ϕ(n) − 1.
Mandal Sagar
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Computing sums in terms of beta, polygamma, and Gauss hypergeometric functions. [PDF]

Rev R Acad Cienc Exactas Fis Nat A Mat, 2020
Qi F, Huang CJ.
europepmc   +1 more source