@article{Ma2022, 
author = {Shunqi Ma},
title = {On the distribution of    k-full lattice points in              Z        2},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {6},
pages = {10596-10608},
keywords = {k-full lattice points, k-full number, density, random walk, two-dimensional integer lattice},
url = {https://www.sciopen.com/article/10.3934/math.2022591},
doi = {10.3934/math.2022591},
abstract = {Let              Z        2   be the two-dimensional integer lattice. For an integer    k  ≥  2, we say a non-zero lattice point in              Z        2   is    k-full if the greatest common divisor of its coordinates is a    k-full number. In this paper, we first prove that the density of    k-full lattice points in              Z        2   is        c    k    =      ∏          p        (  1  −      p          −      2        +      p          −      2      k        ), where the product runs over all primes. Then we show that the density of    k-full lattice points on a path of an    α-random walk in              Z        2   is almost surely        c    k  , which is independent on    α.}
}