summary:Let $[x]$ be an integer part of $x$ and $d(n)$ be the number of positive divisor of $n$. Inspired by some results of M. Jutila (1987), we prove that for $1<c<\frac 65$, $$ \sum _{n\leq x} d([n^c])= cx\log x +(2\gamma -c)x+O\Bigl (\frac {x}{\log x}\Bigr ), $$ where $\gamma $ is the Euler constant and $[n^c]$ is the Piatetski-Shapiro sequence. This gives an improvement upon the classical result of this problem
summary:Let $l\geqslant 2$ be an integer. Recently, Hu and Lü offered the asymptotic formula for the...
Let N(n < x: P) denote the number of positive integers n ^ x with the property P. In an earlier p...
A Lucas sequence is a binary recurrence sequences that includes as special cases, the Pell, the asso...
The divisor function $\tau(n)$ counts the number of positive divisors of an integer n. We are concer...
AbstractLet σ(n) be the sum of the positive divisors of the positive integer n. We give an elementar...
summary:Let $\mathbb {N}$ be the set of positive integers and let $s\in \mathbb {N}$. We denote by $...
summary:Let $$ T(q)=\sum _{k=1}^\infty d(k) q^k, \quad |q|<1, $$ where $d(k)$ denotes the number of ...
International audienceGiven a multiplicative function~$f$ which is periodic over the primes, we obta...
summary:We use the estimation of the number of integers $n$ such that $\lfloor n^c \rfloor $ belongs...
summary:A natural number $n$ is said to be a $(k,r)$-integer if $n=a^kb$, where $k>r>1$ and $b$ is n...
In this paper we sharpen Hildebrand’s earlier result on a conjecture of Erdos on limit points of t...
AbstractLet 1=d1(n)<d2(n)<⋯<dτ(n)=n be the sequence of all positive divisors of the integer n in inc...
ABSTRACT. Let n be a positive integer, Pd(n) denotes the product of all positive divisors of n, qd(n...
The asymptotical formula obtaining for the quantity of divisors of numbers [n_c], c<1, n greater ...
Let {a_{1}(n)}_{n>1} be a purely periodic sequence of nonnegative integers, not identically zero, an...
summary:Let $l\geqslant 2$ be an integer. Recently, Hu and Lü offered the asymptotic formula for the...
Let N(n < x: P) denote the number of positive integers n ^ x with the property P. In an earlier p...
A Lucas sequence is a binary recurrence sequences that includes as special cases, the Pell, the asso...
The divisor function $\tau(n)$ counts the number of positive divisors of an integer n. We are concer...
AbstractLet σ(n) be the sum of the positive divisors of the positive integer n. We give an elementar...
summary:Let $\mathbb {N}$ be the set of positive integers and let $s\in \mathbb {N}$. We denote by $...
summary:Let $$ T(q)=\sum _{k=1}^\infty d(k) q^k, \quad |q|<1, $$ where $d(k)$ denotes the number of ...
International audienceGiven a multiplicative function~$f$ which is periodic over the primes, we obta...
summary:We use the estimation of the number of integers $n$ such that $\lfloor n^c \rfloor $ belongs...
summary:A natural number $n$ is said to be a $(k,r)$-integer if $n=a^kb$, where $k>r>1$ and $b$ is n...
In this paper we sharpen Hildebrand’s earlier result on a conjecture of Erdos on limit points of t...
AbstractLet 1=d1(n)<d2(n)<⋯<dτ(n)=n be the sequence of all positive divisors of the integer n in inc...
ABSTRACT. Let n be a positive integer, Pd(n) denotes the product of all positive divisors of n, qd(n...
The asymptotical formula obtaining for the quantity of divisors of numbers [n_c], c<1, n greater ...
Let {a_{1}(n)}_{n>1} be a purely periodic sequence of nonnegative integers, not identically zero, an...
summary:Let $l\geqslant 2$ be an integer. Recently, Hu and Lü offered the asymptotic formula for the...
Let N(n < x: P) denote the number of positive integers n ^ x with the property P. In an earlier p...
A Lucas sequence is a binary recurrence sequences that includes as special cases, the Pell, the asso...
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