Investigation of divisibility properties of natural numbers is one of themost important themes in the theory of numbers. Various tools have beendeveloped over the centuries to discover and study the various patterns in thesequence of natural numbers in the context of divisibility. In the presentpaper, we study the divisibility of natural numbers using the framework of agrowing complex network. In particular, using tools from the field ofstatistical inference, we show that the network is scale-free but has anon-stationary degree distribution. Along with this, we report a new kind ofsimilarity pattern for the local clustering, which we call "stretchingsimilarity", in this network. We also show that the various characteristicslike average degree, global clustering coefficient and assortativitycoefficient of the network vary smoothly with the size of the network. Usinganalytical arguments we estimate the asymptotic behavior of global clusteringand average degree which is validated using numerical analysis.
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