scholarly journals Number of prime divisors in a product of consecutive integers

2004 ◽  
Vol 113 (4) ◽  
pp. 327-341 ◽  
Author(s):  
Shanta Laishram ◽  
T. N. Shorey
Keyword(s):  
Prime Divisors ◽  
Consecutive Integers ◽  
Number Of Prime Divisors

scholarly journals On the number of prime divisors of the order of elliptic curves modulo p

2005 ◽  
Vol 117 (4) ◽  
pp. 341-352 ◽  
Author(s):  
Jörn Steuding ◽  
Annegret Weng
Keyword(s):  
Elliptic Curves ◽  
Prime Divisors ◽  
Modulo P ◽  
Number Of Prime Divisors

scholarly journals The distribution of the number of prime divisors of sums a + b

1988 ◽  
Vol 29 (1) ◽  
pp. 94-99 ◽  
Author(s):  
P.D.T.A Elliott ◽  
A Sárközy
Keyword(s):  
Prime Divisors ◽  
Number Of Prime Divisors

On the Normal Growth of Prime Factors of Integers

1992 ◽  
Vol 44 (6) ◽  
pp. 1121-1154 ◽  
Author(s):  
J. M. De Koninck ◽  
I. Kátai ◽  
A. Mercier
Keyword(s):  
Prime Factor ◽  
Continuous Distribution ◽  
Normal Growth ◽  
Distribution Functions ◽  
Prime Divisors ◽  
Simple Argument ◽  
Prime Factors ◽  
Almost All ◽  
Number Of Prime Divisors ◽  
Class Of Functions

AbstractLet h: [0,1] → R be such that and define .In 1966, Erdős [8] proved that holds for almost all n, which by using a simple argument implies that in the case h(u) = u, for almost all n, He further obtained that, for every z > 0 and almost all n, and that where ϕ, ψ, are continuous distribution functions. Several other results concerning the normal growth of prime factors of integers were obtained by Galambos [10], [11] and by De Koninck and Galambos [6].Let χ = ﹛xm : w ∈ N﹜ be a sequence of real numbers such that limm→∞ xm = +∞. For each x ∈ χ let be a set of primes p ≤x. Denote by p(n) the smallest prime factor of n. In this paper, we investigate the number of prime divisors p of n, belonging to for which Th(n,p) > z. Given Δ < 1, we study the behaviour of the function We also investigate the two functions , where, in each case, h belongs to a large class of functions.

scholarly journals On the maximal length of two sequences of consecutive integers with the same prime divisors

1989 ◽  
Vol 54 (3-4) ◽  
pp. 225-236 ◽  
Author(s):  
R. Balasubramanian ◽  
T. N. Shorey ◽  
M. Waldschmidt
Keyword(s):  
Maximal Length ◽  
Prime Divisors ◽  
Consecutive Integers

scholarly journals On the residue class distribution of the number of prime divisors of an integer

2011 ◽  
Vol 202 ◽  
pp. 15-22 ◽  
Author(s):  
Michael Coons ◽  
Sander R. Dahmen
Keyword(s):  
Positive Integer ◽  
Error Term ◽  
Residue Class ◽  
Prime Divisors ◽  
Class Distribution ◽  
Multiplicity One ◽  
Counting Multiplicity ◽  
Number Of Prime Divisors

AbstractLet Ω(n) denote the number of prime divisors of n counting multiplicity. One can show that for any positive integer m and all j = 0,1,…,m – 1, we havewith α = 1. Building on work of Kubota and Yoshida, we show that for m > 2 and any j = 0,1,…,m – 1, the error term is not o(xα) for any α < 1.

Sign in / Sign up

Export Citation Format

Share Document