Name
Abstract | ||
|---|---|---|
For a positive integer m, let ω(m) denote the number of distinct prime factors of m. Let h(n) be a function defined on the set of positive integers such that h(n) → ∞ as n → ∞ and let En(h) = {d:d is a positive integer, d ≤ n, ω(d) ≥ h(n)}. Writing Δn = {(x,y):x,y are integers, 1 ≤ x, y ≤ n}, in the present paper we show that one can give explicit description of a set Xn ⊂ Δn such that Δn is visible from Xn with at most 100|En(h)|2 exceptional points and for all sufficiently large n, one has Xn| ≤ 800h(n)log log h(n).As a corollary it follows that one can give explicit description of a set Yn ⊂ Δn such that for large n's, Δn is visible except for at most 100n2(log log n)2 exceptional points from Yn where Yn satisfies |Yn| = O((log logn)(log log log log n)). |
Year | DOI | Venue |
|---|---|---|
2002 | 10.1016/S0012-365X(02)00301-1 | Discrete Mathematics |
Keywords | DocType | Volume |
set yn,log log n,positive integer,yn satisfies,log logn,explicit description,log log h,lattice point,log log log log,large n,exceptional point | Journal | 259 |
Issue | ISSN | Citations |
1-3 | Discrete Mathematics | 1 |
PageRank | References | Authors |
0.71 | 1 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Sukumar Das Adhikari | 1 | 23 | 6.47 |
| Yong-Gao Chen | 2 | 20 | 11.25 |