O číslech spřízněných a dokonalých. [II.]
O elementárním důkazu prvočíselné věty
O osmém Hilbertově problému
Obere Abschätzung für die Anzahl der B-Zwillinge auf kurzen Intervallen.
Odd values of the Ramanujan -function
On 4/n = 1/x + 1/y + 1/z and Rosser's sieve
On a Brun-Titchmarsh inequality for multiplicative functions
On a certain additive function on the Gaussian integers
On a certain class of arithmetic functions
A homothetic arithmetic function of ratio is a function such that for every . Periodic arithmetic funtions are always homothetic, while the converse is not true in general. In this paper we study homothetic and periodic arithmetic functions. In particular we give an upper bound for the number of elements of in terms of the period and the ratio of .
On a class of arithmetic convolutions involving arbitrary sets of integers.
On a class of arithmetical functions connected with multiplicative functions.
On a conjecture of Erdös
On a conjecture of Issai Schur.
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 conjecture of Narkiewicz about functions with non-decreasing normal order
On a conjecture of Pomerance
On a density problem of Erdös
On a divisor problem related to the Epstein zeta-function, IV
On a generalization of a formula of Sierpiński.
On a generalization of a formula of Sierpiński. II.