Results 41 to 50 of about 31,249 (173)
Some problems of Erdős on the sum-of-divisors function [PDF]
Transactions of the American Mathematical Society, Series B, 2016 Let σ ( n ) \sigma (n) denote the sum of all of the positive divisors of n n , and let s ( n ) = σ ( n ) − n s(n) = \sigma (n)-n denote the sum of the proper divisors of n n .
Pollack, Paul, Pomerance, Carl
openaire +1 more source
Values of Arithmetical Functions Equal to a Sum of Two Squares [PDF]
, 2005 http://www.math.missouri.edu/~bbanks/papers/index.htmlLet '(n) denote the Euler function. In this paper, we determine the order of growth for the number of positive integers n ≤ x for which '(n) is the sum of two square numbers.
Banks, William David, 1964- +3 more
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Wheat flour particle size: Influence of mill design and effects on quality and performance
JSFA reports, EarlyView.Abstract Among the various characteristics of wheat (Triticum aestivum) flour, particle size is of paramount importance globally. The industrial process of separating the three main components (endosperm, bran, and germ) must ensure that the desired quality is delivered to customers through a progressive reduction in the size of the endosperm until the
Ricardo Barroso Lopes +3 more
wiley +1 more source
On the ratio of the sum of divisors and Euler’s Totient Function I [PDF]
, 2013 We prove that the only solutions to the equation σ(n)=2φ(n) with at most three distinct prime factors are 3, 35 and 1045. Moreover, there exist at most a finite number of solutions to σ(n)=2φ(n) with Ω(n)≤ k, and there are at most 22k+k-k squarefree ...
Broughan, Kevin A., Delbourgo, Daniel
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A Novel Two‐Stage Flexible Flow Shop Batch Scheduling Model for Grinding Workshops
Naval Research Logistics (NRL), EarlyView.ABSTRACT The growing need for data storage in data centers has increased the demand for mechanical hard disks due to their low cost and high reliability. Aluminum substrates are the most popular base plates for mechanical hard disks because of their high hardness and low cost.
Jun Xu +4 more
wiley +1 more source
On the ratio of the sum of divisors and Euler’s totient function II [PDF]
, 2014 We find the form of all solutions to ø(n) | σ(n) with three or fewer prime factors, except when the quotient is 4 and n is ...
Broughan, Kevin A., Zhou, Qizhi
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Branes, Black Holes and Topological Strings on Toric Calabi-Yau Manifolds
, 2005 We develop means of computing exact degerenacies of BPS black holes on toric Calabi-Yau manifolds. We show that the gauge theory on the D4 branes wrapping ample divisors reduces to 2D q-deformed Yang-Mills theory on necklaces of P^1's.
A. Dabholkar +17 more
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Quarterly Journal of the Royal Meteorological Society, EarlyView.We investigate whether Central European heatwaves (HWs) forming under omega blocking differ from those enabled by subtropical ridges, in terms of both air‐mass origin and processes warming air parcels along their way. Using ERA5‐based backward trajectories and a Lagrangian temperature anomaly decomposition, we identify significant differences in the ...
Alexander Lemburg +3 more
wiley +1 more source
n-Color partitions with weighted differences equal to minus two
International Journal of Mathematics and Mathematical Sciences, 1997 In this paper we study those n-color partitions of Agarwal and Andrews, 1987, in which each pair of parts has weighted difference equal to −2 Results obtained in this paper for these partitions include several combinatorial identities, recurrence ...
A. K. Agarwal, R. Balasubrananian
doaj +1 more source
The sum of the unitary divisor function [PDF]
, 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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