The reciprocal sum of the amicable numbers

2018 ◽  
Vol 88 (317) ◽  
pp. 1503-1526 ◽  
Author(s):  
Hanh My Nguyen ◽  
Carl Pomerance
Keyword(s):  
Reciprocal Sum

An upper estimate for the reciprocal sum of a sum-free sequence

1977 ◽  
Vol 34 (1) ◽  
pp. 9-24 ◽  
Author(s):  
Eugene Levine ◽  
Joseph O'Sullivan
Keyword(s):  
Reciprocal Sum ◽  
Upper Estimate

On the partitions into squares whose reciprocal sum is one

2019 ◽  
Vol 95 (1-2) ◽  
pp. 243-247
Author(s):  
Byungchan Kim ◽  
Ji Young Kim ◽  
Chong Gyu Lee ◽  
Poo-Sung Park
Keyword(s):  
Reciprocal Sum

scholarly journals Some results on the reciprocal sum-degree distance of graphs

2013 ◽  
Vol 30 (3) ◽  
pp. 435-446 ◽  
Author(s):  
Guifu Su ◽  
Liming Xiong ◽  
Xiaofeng Su ◽  
Xianglian Chen
Keyword(s):  
Degree Distance ◽  
Reciprocal Sum

scholarly journals A $B\sb 2$-sequence with larger reciprocal sum

1993 ◽  
Vol 60 (202) ◽  
pp. 835-835
Author(s):  
Zhen Xiang Zhang
Keyword(s):  
Reciprocal Sum

scholarly journals On the reciprocal sum of sum-free sequences

2014 ◽  
Vol 44 (2) ◽  
pp. 117-126
Author(s):  
JianDong WU
Keyword(s):  
Reciprocal Sum

On the reciprocal sum of a sum-free sequence

2012 ◽  
Vol 56 (5) ◽  
pp. 951-966 ◽  
Author(s):  
YongGao Chen
Keyword(s):  
Reciprocal Sum

EIGENTIME IDENTITY FOR WEIGHT-DEPENDENT WALK ON A CLASS OF WEIGHTED FRACTAL SCALE-FREE HIERARCHICAL-LATTICE NETWORKS

Fractals ◽  
2019 ◽  
Vol 27 (08) ◽  
pp. 1950138
Author(s):  
BO WU ◽  
ZHIZHUO ZHANG ◽  
YINGYING CHEN ◽  
TINGTING JU ◽  
MEIFENG DAI ◽  
...  
Keyword(s):  
Iteration Process ◽  
Laplacian Matrix ◽  
Network Size ◽  
Hierarchical Lattice ◽  
Analytical Expression ◽  
Scale Free ◽  
Scale Free Networks ◽  
Reciprocal Sum ◽  
Successive Generations ◽  
Relationship Of

In this paper, we construct a class of weighted fractal scale-free hierarchical-lattice networks. Each edge in the network generates [Formula: see text] connected branches in each iteration process and assigns the corresponding weight. To reflect the global characteristics of such networks, we study the eigentime identity determined by the reciprocal sum of non-zero eigenvalues of normalized Laplacian matrix. By the recursive relationship of eigenvalues at two successive generations, we find the eigenvalues and their corresponding multiplicities for two cases when [Formula: see text] is even or odd. Finally, we obtain the analytical expression of the eigentime identity and the scalings with network size of the weighted scale-free networks.

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