Large and small gaps between consecutive Niven numbers.
On a sum of divisors problem.
On strings of consecutive economical numbers of arbitrary length.
Some remarks on a paper of L. Tóth.
Partial sums of powers of prime factors.
Positive integers such that .
On the difference of values of the kernel function at consecutive integers.
On a thin set of integers involving the largest prime factor function.
Powerful values of quadratic polynomials.
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.
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