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A Triangular Array of the Counts of Natural Numbers with the Same Number of Prime Factors (Dimensions) Within 2n Space

2014/01/07 by Ran Huang, Huang, Ran
Mathematics · #FOS: Mathematics #General Mathematics (math.GM) #math.GM

paper · pdf · doi:10.48550/arxiv.1401.2360

13 pages, 8 figures

arxiv created 2014/01/07 · arxiv updated 2014/01/13

Abstract

By defining the dimension of natural numbers as the number of prime factors, all natural numbers smaller than 2^(n+1) (n is a natural number) can be classified by their dimensions, and the count of numbers of each dimension gives a dimensions distribution directly related to the distribution of prime numbers. A triangle similar to Pascals triangle from some aspects can be obtained by the ensemble of dimensions distributions. Some superficial explorations have been done to this interesting triangle.

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