Results 21 to 30 of about 31,208 (175)
Nonaliquots and Robbins Numbers [PDF]
, 2005 http://www.math.missouri.edu/~bbanks/papers/index.htmlLet '(•) and _(•) denote the Euler function and the sum of divisors function, respectively. In this paper, we give a lower bound for the number of m ≤ x for which the equation m = _(n)−n has no ...
Banks, William David, 1964- +1 more
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Arithmetic functions associated with infinitary divisors of an integer
International Journal of Mathematics and Mathematical Sciences, 1993 The infinitary divisors of a natural number n are the products of its divisors of the form pyα2α, where py is a prime-power component of n and ∑αyα2α (where yα=0 or 1) is the binary representation of y.
Graeme L. Cohen, Peter Hagis
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On the average value of the least common multiple of k positive integers [PDF]
, 2016 We deduce an asymptotic formula with error term for the sum ∑n1,…,nk≤xf([n1,…,nk]), where [n1,…,nk] stands for the least common multiple of the positive integers n1,…,nk (k≥2) and f belongs to a large class of multiplicative arithmetic functions ...
Alladi +24 more
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Zaremba’s conjecture and sums of the divisor function [PDF]
Mathematics of Computation, 1993 Zaremba conjectured that given any integer m > 1 m > 1 , there exists an integer a > m a > m with a relatively prime to m such that the simple continued fraction [ 0 , c 1 ,
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Arithmatical consequences of two identities of B. Gordon
International Journal of Mathematics and Mathematical Sciences, 1979 From two partition identities of Basil Gordon the author derives two recursive formulas for the sum-of-divisors function. A third application yields an alternate proof of Rmanujan's theorem on the divisibility of certain values of the partition function ...
John A. Ewell
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Variations on a theorem of Davenport concerning abundant numbers [PDF]
, 2013 Let \sigma(n) = \sum_{d \mid n}d be the usual sum-of-divisors function. In 1933, Davenport showed that that n/\sigma(n) possesses a continuous distribution function. In other words, the limit D(u):= \lim_{x\to\infty} \frac{1}{x}\sum_{n \leq x,~n/\sigma(n)
Jennings, Emily +2 more
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The Nicolas and Robin inequalities with sums of two squares [PDF]
, 2007 In 1984, G. Robin proved that the Riemann hypothesis is true if and only if the Robin inequality $\sigma(n)5040$, where $\sigma(n)$ is the sum of divisors function, and $\gamma$ is the Euler-Mascheroni constant.
Banks, William D. +3 more
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Recursive Determination of the Sum-of-Divisors Function [PDF]
Proceedings of the American Mathematical Society, 1979 A recursive scheme for determination of the sum-of-divisors function is presented. As all of the formulas involve triangular numbers, the scheme is therefore compared for efficiency with another known recursive triangular-number formula for this function.
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Divisor Functions and the Number of Sum Systems [PDF]
, 2019 Divisor functions have attracted the attention of number theorists from Dirichlet to the present day. Here we consider associated divisor functions $c_j^{(r)}(n)$ which for non-negative integers $j, r$ count the number of ways of representing $n$ as an ordered product of $j+r$ factors, of which the first $j$ must be non-trivial, and their natural ...
Lettington, Matthew C. +1 more
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Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2014 We obtain an arithmetic proof and a refinement of the inequality ϕ (nk) + σk(n) < 2nk, where n ≧ 2 and k ≧ 2. An application to another inequality is also provided.
Sándor József
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