Results 1 to 10 of about 31,208 (175)
On a Sum Involving the Sum-of-Divisors Function [PDF]
Journal of Mathematics, 2021 Let σn be the sum of all divisors of n and let t be the integral part of t. In this paper, we shall prove that ∑n≤xσx/n=π2/6x log x+Oxlog x2/3log2 x4/3 for x⟶∞, and that the error term of this asymptotic formula is Ωx.
Feng Zhao, Jie Wu
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The sum of the unitary divisor function [PDF]
Publications de l'Institut Mathematique, 2014 This article establishes a new upper bound on the function $\sigma^{*}(n)$, the sum of all coprime divisors of $n$. The article concludes with two questions concerning this function.Comment: 6 pages, to appear in Publ. Inst. Math. (Beograd) (N.S.
Trudgian, Tim
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Iterating the Sum-of-Divisors Function [PDF]
Experimental Mathematics, 1996 Let $\sigma^0(n) = n$ and $\sigma^m(n) = \sigma(\sigma^{m-1}(n))$, where $m\ge1$ and $\sigma$ is the sum-of-divisors function. We say that $n$ is $(m,k)$-perfect if $\sigma^m(n) = kn$. We have tabulated all $(2,k)$-perfect numbers up to $10^9$ and all $(3,k)$- and $(4,k)$-perfect numbers up to $2\cdot10^8$.
Cohen, Graeme L., te Riele, Herman J. J.
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On a modification of Set(n) [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 A modification of the set Set(n) for a fixed natural number n is introduced in the form: Set(n, f), where f is an arithmetic function. The sets Set(n,φ), Set(n,ψ), Set(n,σ) are discussed, where φ, ψ and σ are Euler's function, Dedekind's function and the
Krassimir T. Atanassov, József Sándor
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The Dirichlet divisor problem over square-free integers and unitary convolutions [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 We obtain an asymptotic formula for the sum ~D₂ of the divisors of all square-free integers less than or equal to x, with error term O(x^{1/2 + ε}). This improves the error term O(x^{3/4 + ε}) presented in [7] obtained via analytical methods.
André Pierro de Camargo
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INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER RESEARCH, 2023 We show that the recurrence relation deduced by Robbins and Osler et al for the sum of divisors function can be solved in terms of the complete Bell polynomials. Besides, the connection between and the number of representations of n as the sum of four triangular numbers allows obtain arecurrence relation where only participate the values of with m
R. Sivaraman +2 more
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ON A SUM INVOLVING CERTAIN ARITHMETIC FUNCTIONS ON PIATETSKI–SHAPIRO AND BEATTY SEQUENCES
Проблемы анализа, 2022 Let 𝑐, 𝛼, 𝛽 ∈ R be such that ...
T. Srichan
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On the sum of positive divisors functions [PDF]
Research in Number Theory, 2021 AbstractProperties of divisor functions $$\sigma _k(n)$$ σ k ( n ) , defined as sums of k-th powers of all
Radek Erban, Robert A. Van Gorder
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Density bounds for the sum of divisors function [PDF]
Mathematics of Computation, 1972 Upper and lower bounds are presented for the density of the integers n n for which σ ( n ) / n ≧ x \sigma (n)/n \geqq x , where σ ( n ) \sigma (n) is the sum of divisors of n n , and
Wall, Charles R. +2 more
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Inequalities between some arithmetic functions, II [PDF]
Notes on Number Theory and Discrete MathematicsAs a continuation of Part I (see [1]), we offer new inequalities for classical arithmetic functions such as the Euler's totient function, the Dedekind's psi function, the sum of the positive divisors function, the number of divisors function, extended ...
Krassimir Atanassov +2 more
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