Results 1 to 10 of about 56 (56)
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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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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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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Completely multiplicative functions arising from simple operations
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 9, Page 431-441, 2004., 2004 Given two multiplicative arithmetic functions, various conditions for their convolution, powers, and logarithms to be completely multiplicative, based on values at the primes, are derived together with their applications.
Vichian Laohakosol, Nittiya Pabhapote
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A rationality condition for the existence of odd perfect numbers
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 20, Page 1261-1293, 2003., 2003 A rationality condition for the existence of odd perfect numbers is used to derive an upper bound for the density of odd integers such that σ(N) could be equal to 2N, where N belongs to a fixed interval with a lower limit greater than 10300. The rationality of the square root expression consisting of a product of repunits multiplied by twice the base ...
Simon Davis
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Some characterizations of specially multiplicative functions
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 37, Page 2335-2344, 2003., 2003 A multiplicative function f is said to be specially multiplicative if there is a completely multiplicative function fA such that f(m)f(n) = ∑d|(m,n)f(mn/d2)fA(d) for all m and n. For example, the divisor functions and Ramanujan′s τ‐function are specially multiplicative functions. Some characterizations of specially multiplicative functions are given in
Pentti Haukkanen
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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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On the difference of values of the kernel function at consecutive integers
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 67, Page 4249-4262, 2003., 2003 For each positive integer n, set γ(n) = Πp|np. Given a fixed integer k ≠ ±1, we establish that if the ABC‐conjecture holds, then the equation γ(n + 1) − γ(n) = k has only finitely many solutions. In the particular cases k = ±1 , we provide a large family of solutions for each of the corresponding equations.
Jean-Marie De Koninck, Florian Luca
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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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Characterizing completely multiplicative functions by generalized Möbius functions
International Journal of Mathematics and Mathematical Sciences, Volume 29, Issue 11, Page 633-639, 2002., 2002 Using the generalized Möbius functions, μα, first introduced by Hsu (1995), two characterizations of completely multiplicative functions are given; save a minor condition they read (μαf)−1=μ−αf and fα = μ−αf.
Vichian Laohakosol +2 more
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