Additive functions monotonic on the set of primes
Cesàro means related to the square of the divisor function
Composite positive integers with an average prime factor
Convoluted convolved Fibonacci numbers.
Distribution functions of the sequence as go to infinity.
Distribution of arithmetical functions. A survey
Eine Anwendungen Tauberscher Sätze in der Zahlentheorie. A.
Einige Anwendungen Tauberscher Sätze in der Zahlentheorie. B.
Errata to: Comparison of regular convolutions.
Long gaps between deficient numbers
Module de continuité de la fonction de répartition de φ(n)/n
Moment convergence and the law of iterated logarithm for additive functions
Multiplicative functions with difference tending to zero
On a conjecture of Mąkowski and Schinzel concerning the composition of the arithmetic functions σ and ϕ
For any positive integer n let ϕ(n) and σ(n) be the Euler function of n and the sum of divisors of n, respectively. In [5], Mąkowski and Schinzel conjectured that the inequality σ(ϕ(n)) ≥ n/2 holds for all positive integers n. We show that the lower density of the set of positive integers satisfying the above inequality is at least 0.74.
On a multiplicative partition function.
On distribution of arithmetical functions on the set prime plus one
On the arithmetic structure of the integers whose sum of digits is fixed
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.
On the concentration of certain additive functions
We study the concentration of the distribution of an additive function f when the sequence of prime values of f decays fast and has good spacing properties. In particular, we prove a conjecture by Erdős and Kátai on the concentration of when c > 1.
On the DDT theorem