Sur les plus grands facteurs premiers d'un entier.
Sur le plus grand facteur premier
Sums of Periodicals of Certain Additive Functions.
Les fonctions arithmétiques et le plus grand facteur premier
Sums involving the largest prime divisor of an integer
Arithmetic functions and weighted averages
On the distribution of subsets of primes in the prime factorization of integers
Exponential sums involving the largest prime factor function
Sur la proximité des nombres puissants
Normal numbers and the middle prime factor of an integer
Let pₘ(n) stand for the middle prime factor of the integer n ≥ 2. We first establish that the size of log pₘ(n) is close to √(log n) for almost all n. We then show how one can use the successive values of pₘ(n) to generate a normal number in any given base D ≥ 2. Finally, we study the behavior of exponential sums involving the middle prime factor function.
On the composition of the Euler function and the sum of divisors function
Let H(n) = σ(ϕ(n))/ϕ(σ(n)), where ϕ(n) is Euler's function and σ(n) stands for the sum of the positive divisors of n. We obtain the maximal and minimal orders of H(n) as well as its average order, and we also prove two density theorems. In particular, we answer a question raised by Golomb.
Shifted values of the largest prime factor function and its average value in short intervals
We obtain estimates for the average value of the largest prime factor P(n) in short intervals [x,x+y] and of h(P(n)+1), where h is a complex-valued additive function or multiplicative function satisfying certain conditions. Letting stand for the sum of the digits of n in base q ≥ 2, we show that if α is an irrational number, then the sequence is uniformly distributed modulo 1.
On the Coprimality of Some Arithmetic Functions
Sommes de Reciproques de Grandes Fonctions Additives
On the counting function for the Niven numbers
Sur la quantité de nombres économiques
On the unimodal character of the frequency function of the largest prime factor
The main objective of this paper is to analyze the unimodal character of the frequency function of the largest prime factor. To do that, let P(n) stand for the largest prime factor of n. Then define f(x,p): = #{n ≤ x | P(n) = p}. If f(x,p) is considered as a function of p, for 2 ≤ p ≤ x, the primes in the interval [2,x] belong to three intervals I₁(x) = [2,v(x)], I₂(x) = ]v(x),w(x)[ and I₃(x) = [w(x),x], with v(x) < w(x), such that f(x,p) increases for p ∈ I₁(x), reaches its maximum value in...
Bounds for the counting function of the Jordan-Pólya numbers
A positive integer is said to be a Jordan-Pólya number if it can be written as a product of factorials. We obtain non-trivial lower and upper bounds for the number of Jordan-Pólya numbers not exceeding a given number .
Large and small gaps between consecutive Niven numbers.
On a sum of divisors problem.
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