Results 11 to 20 of about 31,249 (173)
On power values of sum of divisors function in arithmetic progressions
Indian Journal of Pure and Applied Mathematics, 2023 8 pages, submitted to Mediterranean Journal of ...
Sai Teja Somu, Vidyanshu Mishra
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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 number of prime factors of values of the sum-of-proper-divisors function [PDF]
Journal of Number Theory, 2015 Let $\omega(n)$ (resp. $\Omega(n)$) denote the number of prime divisors (resp. with multiplicity) of a natural number $n$. In 1917, Hardy and Ramanujan proved that the normal order of $\omega(n)$ is $\log\log n$, and the same is true of $\Omega(n ...
Troupe, Lee
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The algebraic independence of the sum of divisors functions
Journal of Number Theory, 2010 Let \(\sigma_j(n)=\sum_{d|n}d^j\) be the sum of divisors function, and let \(I\) be the identity function. The author shows that the set of functions \(\{\sigma_i\}_{i=0}^\infty\cup \{I\}\) is algebraically independent. Let \(\pi\) be a prime, \(s\) be an integer relatively prime to \(\pi\), \(\alpha\) be a nonnegative integer, \(r=\pi^\alpha s\) and \(
Daniel Lustig
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Euler's function and the sum of divisors.
Journal für die reine und angewandte Mathematik (Crelles Journal), 1981 openaire +3 more sources
Dynamic multi‐objective optimisation of complex networks based on evolutionary computation
IET Networks, EarlyView., 2022 Abstract As the problems concerning the number of information to be optimised is increasing, the optimisation level is getting higher, the target information is more diversified, and the algorithms are becoming more complex; the traditional algorithms such as particle swarm and differential evolution are far from being able to deal with this situation ...
Linfeng Huang
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On the composition of the Euler function and the sum of divisors function [PDF]
Colloquium Mathematicum, 2007 Jean-Marie De Koninck, Florian Luca
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N $$ \mathcal{N} $$ = 2* Schur indices
Journal of High Energy Physics, 2023 We find closed-form expressions for the Schur indices of 4d N $$ \mathcal{N} $$ = 2* super Yang-Mills theory with unitary gauge groups for arbitrary ranks via the Fermi-gas formulation. They can be written as a sum over the Young diagrams associated with
Yasuyuki Hatsuda, Tadashi Okazaki
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Average order of the divisor functions with negative power weight [PDF]
, 1993 In this paper we are primarily concerned with the study of the sums of the sum-of-divisors function σn(n) with negative power weight n-1(t>0), i.e. the sums of the form ..
Ishibashi Makoto
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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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