On sequences of positive integers
On Sidon sequences of even orders
On some Formulas Involving !n and the Verification of the !n-hypothesis by use of Computers
On some Markov matrices arising from the generalized Collatz mapping
On some properties of Chebyshev polynomials
Letting (resp. ) be the n-th Chebyshev polynomials of the first (resp. second) kind, we prove that the sequences and for n - 2⎣n/2⎦ ≤ k ≤ n - ⎣n/2⎦ are two basis of the ℚ-vectorial space formed by the polynomials of ℚ[X] having the same parity as n and of degree ≤ n. Also and admit remarkableness integer coordinates on each of the two basis.
On sums of distinct representatives
On ternary inclusion-exclusion polynomials.
On the (3N+1)-conjecture
On the central coefficients of Bell matrices.
On the Collatz conjecture
We propose two conjectures which imply the Collatz conjecture. We give a numerical evidence for the second conjecture.
On the difference of consecutive terms of sequences defined by divisibility properties, II
On the difference of consecutive terms of sequences defined by divisibility properties
On the distribution of arithmetic functions
On the distribution of multiplicative arithmetical functions
On the distribution of the distances of multiples of an irrational number to the nearest integer
On the divisibility properties of integers (I)
On the divisibility properties of sequences of integers (II)
On the divisor function over Piatetski-Shapiro sequences
Let be an integer part of and be the number of positive divisor of . Inspired by some results of M. Jutila (1987), we prove that for , where is the Euler constant and is the Piatetski-Shapiro sequence. This gives an improvement upon the classical result of this problem.
On the divisors of
On the error term of the logarithm of the lcm of a quadratic sequence
We study the logarithm of the least common multiple of the sequence of integers given by . Using a result of Homma [5] on the distribution of roots of quadratic polynomials modulo primes we calculate the error term for the asymptotics obtained by Cilleruelo [3].