Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Triangular Array of the Counts of Natural Numbers with the Same Number
  of Prime Factors (Dimensions) Within 2n Space   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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The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an