On a density problem of Erdös

Safwan Akbik

International Journal of Mathematics and Mathematical Sciences, 1999, vol. 22, 1-4

Abstract:

For a positive integer n , let P ( n ) denotes the largest prime divisor of n and define the set: 𝒮 ( x ) = 𝒮 = { n ≤ x : n does not divide P ( n ) ! } . Paul Erdös has proposed that | S | = o ( x ) as x → ∞ , where | S | is the number of n ∈ S . This was proved by Ilias Kastanas. In this paper we will show the stronger result that | S | = O ( x e − 1 / 4 log x ) .

Date: 1999
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/IJMMS/22/645604.pdf (application/pdf)
http://downloads.hindawi.com/journals/IJMMS/22/645604.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:645604

DOI: 10.1155/S0161171299226555

Access Statistics for this article

More articles in International Journal of Mathematics and Mathematical Sciences from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().