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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 +2 more
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A short note on Layman permutations
Acta Universitatis Sapientiae: Mathematica, 2022 A permutation p of [k] = {1, 2, 3, …, k} is called Layman permutation iff i + p(i) is a Fibonacci number for 1 ≤ i ≤ k. This concept is introduced by Layman in the A097082 entry of the Encyclopedia of Integers Sequences, that is the number of Layman ...
Hajnal Péter
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Acta Universitatis Sapientiae: Mathematica, 2023 In this paper, singularly perturbed differential equations having both small and large delay are considered. The considered problem contains large delay parameter on the reaction term and small delay parameter on the convection term.
Debela Habtamu Garoma +1 more
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Proofs, generalizations and analogs of Menon’s identity: a survey
Acta Universitatis Sapientiae: Mathematica, 2023 Menon’s identity states that for every positive integer n one has ∑ (a − 1, n) = φ (n)τ(n), where a runs through a reduced residue system (mod n), (a − 1, n) stands for the greatest common divisor of a − 1 and n, φ(n) is Euler’s totient function, and τ(n)
Tóth László
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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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Collatz conjecture revisited: an elementary generalization
Acta Universitatis Sapientiae: Mathematica, 2020 Collatz conjecture states that iterating the map that takes even natural number n to n2{n \over 2} and odd natural number n to 3n + 1, will eventually obtain 1. In this paper a new generalization of the Collatz conjecture is analyzed and some interesting
Gutierrez Amauri
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Avian immunoglobulin-producing cell lines [PDF]
, 1991 The present invention involves a method for preparing antibody-producing chicken cell clones. This method comprises a series of steps including initially immunizing a first chicken with a desired antigen.
Humphries, Eric H.
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, 2002 There is a body of work in the literature on various restricted sums of the number of divisors of an integer function including that described in [2-9, 11] and summarised in Section 2 ...
Broughan, Kevin A.
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A Note about Iterated Arithmetic Functions [PDF]
, 2015 Let $f\colon\mathbb{N}\rightarrow\mathbb{N}_0$ be a multiplicative arithmetic function such that for all primes $p$ and positive integers $\alpha$, $f(p^{\alpha})
Defant, Colin
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