On k-triad sequences.
On linear normal lattices configurations
In this paper we extend Champernowne’s construction of normal numbers in base to the case and obtain an explicit construction of the generic point of the shift transformation of the set . We prove that the intersection of the considered lattice configuration with an arbitrary line is a normal sequence in base .
On Lucas pseudoprimes of the form in arithmetic progression with a prescribed value of the Jacobi symbol
On m times covering systems of congruences
On mod logarithms and .
On multiplicatively dependent linear numeration systems, and periodic points
Two linear numeration systems, with characteristic polynomial equal to the minimal polynomial of two Pisot numbers and respectively, such that and are multiplicatively dependent, are considered. It is shown that the conversion between one system and the other one is computable by a finite automaton. We also define a sequence of integers which is equal to the number of periodic points of a sofic dynamical system associated with some Parry number.
On multiplicatively dependent linear numeration systems, and periodic points
Two linear numeration systems, with characteristic polynomial equal to the minimal polynomial of two Pisot numbers β and γ respectively, such that β and γ are multiplicatively dependent, are considered. It is shown that the conversion between one system and the other one is computable by a finite automaton. We also define a sequence of integers which is equal to the number of periodic points of a sofic dynamical system associated with some Parry number.
On multiplicatively e-perfect numbers.
On multiplicatively perfect numbers.
On and .
On near-perfect and deficient-perfect numbers
For a positive integer n, let σ(n) denote the sum of the positive divisors of n. Let d be a proper divisor of n. We call n a near-perfect number if σ(n) = 2n + d, and a deficient-perfect number if σ(n) = 2n - d. We show that there is no odd near-perfect number with three distinct prime divisors and determine all deficient-perfect numbers with at most two distinct prime factors.
On near-perfect numbers
For a positive integer n, let σ(n) denote the sum of the positive divisors of n. We call n a near-perfect number if σ(n) = 2n + d where d is a proper divisor of n. We show that the only odd near-perfect number with four distinct prime divisors is 3⁴·7²·11²·19².
On Newman's conjecture and prime trees.
On numbers containing each block infinitely often.
On Obláth's problem.
On partition functions and divisor sums.
On Pascal’s triangle modulo
On perfect numbers connected with the composition of arithmetic functions.
On perfect totient numbers.
On periodic mod p sequences and G-functions (On a conjecture of Ruzsa).