A Triangular Array of the Counts of Natural Numbers with the Same Number of Prime Factors (Dimensions) Within 2n Space
General Mathematics
2014-01-13 v1
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.
Cite
@article{arxiv.1401.2360,
title = {A Triangular Array of the Counts of Natural Numbers with the Same Number of Prime Factors (Dimensions) Within 2n Space},
author = {Ran Huang},
journal= {arXiv preprint arXiv:1401.2360},
year = {2014}
}
Comments
13 pages, 8 figures