  We propose a new alignment-free algorithm by constructing a compact vector
representation on $\mathbb{R}^{24}$ of a DNA sequence of arbitrary length. Each
component of this vector is obtained from a representative sequence, the
elements of which are the values realized by a function $\Gamma$. $\Gamma$ acts
on neighborhoods of arbitrary radius that are located at strategic positions
within the DNA sequence and carries complete information about the local
distribution of frequencies of the nucleotides as a consequence of the
uniqueness of prime factorization of integer. The algorithm exhibits linear
time complexity and turns out to consume significantly small memory. The two
natural parameters characterizing the radius and location of the neighbourhoods
are fixed by comparing the phylogenetic tree with the benchmark for full genome
sequences of fish mtDNA datasets. Using these fitting parameters, the method is
applied to analyze a number of genome sequences from benchmark and other
standard datasets. The algorithm proves to be computationally efficient
compared to Co-phylog and CD-MAWS when applied over a certain range of a
simulated dataset.
