We study the function O(x, y, z) that counts the number of positive integers n ≤ x which have a divisor d > z with the property that p ≤ y for every prime p dividing d. We also indicate some cryptographic applications of our results.11 page(s
For a positive integer n we let τ(n) denote the number of its positive divisors. In this paper, we o...
AbstractLet d(n) denote the number of positive integers dividing the positive integer n. We show tha...
AbstractLet Q be a set of primes having relative density δ among the primes, with 0<δ<1, and let ψ(x...
We study the function Θ(x, y, z) that counts the number of positive integers n ≤ x which have a divi...
We study the function Θ(x, y, z) that counts the number of positive integers n ≤ x which have a divi...
Abstract. Let P (n) denote the largest prime divisor of n, and let Ψ(x, y) be the number of integers...
AbstractLet 1=d1(n)<d2(n)<⋯<dτ(n)=n be the sequence of all positive divisors of the integer n in inc...
This paper deals with products of moderate-size primes, familiarly known as smooth numbers. Smooth n...
© 2017, Allerton Press, Inc. A natural number n is called y-smooth (y-powersmooth, respectively) for...
© 2016, Pleiades Publishing, Ltd.An integer number n > 0 is called y-smooth for y > 0 if any prime f...
AbstractLet 1=d1(n)<d2(n)<⋯<dτ(n)=n be the sequence of all positive divisors of the integer n in inc...
The principal divisors of a positive integer n are its maximal prime-power divisors. The principal d...
We study the problem of bounding the number of primes p ≤ x in an arithmetic progression for which t...
We establish upper bounds for the number of smooth values of the Euler function. In particular, alth...
In this paper we obtain lower bounds on the set of the largest prime divisors P(a(n)) of various seq...
For a positive integer n we let τ(n) denote the number of its positive divisors. In this paper, we o...
AbstractLet d(n) denote the number of positive integers dividing the positive integer n. We show tha...
AbstractLet Q be a set of primes having relative density δ among the primes, with 0<δ<1, and let ψ(x...
We study the function Θ(x, y, z) that counts the number of positive integers n ≤ x which have a divi...
We study the function Θ(x, y, z) that counts the number of positive integers n ≤ x which have a divi...
Abstract. Let P (n) denote the largest prime divisor of n, and let Ψ(x, y) be the number of integers...
AbstractLet 1=d1(n)<d2(n)<⋯<dτ(n)=n be the sequence of all positive divisors of the integer n in inc...
This paper deals with products of moderate-size primes, familiarly known as smooth numbers. Smooth n...
© 2017, Allerton Press, Inc. A natural number n is called y-smooth (y-powersmooth, respectively) for...
© 2016, Pleiades Publishing, Ltd.An integer number n > 0 is called y-smooth for y > 0 if any prime f...
AbstractLet 1=d1(n)<d2(n)<⋯<dτ(n)=n be the sequence of all positive divisors of the integer n in inc...
The principal divisors of a positive integer n are its maximal prime-power divisors. The principal d...
We study the problem of bounding the number of primes p ≤ x in an arithmetic progression for which t...
We establish upper bounds for the number of smooth values of the Euler function. In particular, alth...
In this paper we obtain lower bounds on the set of the largest prime divisors P(a(n)) of various seq...
For a positive integer n we let τ(n) denote the number of its positive divisors. In this paper, we o...
AbstractLet d(n) denote the number of positive integers dividing the positive integer n. We show tha...
AbstractLet Q be a set of primes having relative density δ among the primes, with 0<δ<1, and let ψ(x...