Sai Teja Somu

activity

20152024

collaborators

13 papers

math.NT2024

On Sums of Practical Numbers and Polygonal Numbers

Sai Teja Somu, Duc Van Khanh Tran

Practical numbers are positive integers $n$ such that every positive integer less than or equal to $n$ can be written as a sum of distinct positive divisors of $n$ . In this paper,…

math.NT2023

Some Results on Zumkeller Numbers

Sai Teja Somu, Andrzej Kukla, Duc Van Khanh Tran

A positive integer $n$ is said to be a Zumkeller number or an integer-perfect number if the set of its positive divisors can be partitioned into two subsets of equal sums. In this…

math.NT2022

On Some Results on Practical Numbers

Sai Teja Somu, Ting Hon Stanford Li, Andrzej Kukla

A positive integer $n$ is said to be a practical number if every integer in $[1, n]$ can be represented as the sum of distinct divisors of $n$ . In this article, we consider practica…

math.NT2022

On Power Values of Sum of Divisors function in Arithmetic Progressions

Sai Teja Somu, Vidyanshu Mishra

Let $a \geq 1, b \geq 0$ and $k \geq 2$ be any given integers. It has been proven that there exist infinitely many natural numbers $m$ such that sum of divisors of $m$ is a perfect $k…

math.GM2021

On a Generalization of Tupper's Formula for $m$ Colours and $n$ Dimensions

Sai Teja Somu, Vidyanshu Mishra

Tupper's formula $\frac{1}{2} < ⌊ mod (⌊ \frac{y}{17} ⌋ 2^{- 17 ⌊ x ⌋ - mod (⌊ y ⌋, 17)}, 2) ⌋$ has an interesting pr…

math.NT2021

On Some Generalizations to Floor Function Identities of Ramanujan

Andrzej Kukla, Sai Teja Somu

We give some generalizations to three identities of Srinivasa Ramanujan involving greatest integer function.

math.NT2018

Additive Complements for a given Asymptotic Density

Alain Faisant, Georges Grekos, Ram Krishna Pandey +1

{The first version of this text was written and submitted to a journal on April, 12, 2018. This second version was submitted on April, 9, 2019.} We investigate the existence of sub…

math.NT2017

On $r t h$ coefficient of divisors of $x^{n} - 1$

Sai Teja Somu

Let $r, n$ be two natural numbers and let $H (r, n)$ denote the maximal absolute value of $r$ th coefficient of divisors of $x^{n} - 1$ . In this paper, we show that $\sum_{n \leq x} H (r, n)$ …

math.NT2015

On the coefficients of divisors of $x^{n} - 1$

Sai Teja Somu

Let $a (r, n)$ be $r$ th coefficient of $n$ th cyclotomic polynomial. Suzuki proved that ${a (r, n) ∣ r \geq 1, n \geq 1} = Z$ . If $m$ and $n$ are two natural numbers we prove an ana…

math.NT2015

On unavoidable obstructions in Gaussian walks

Sai Teja Somu, Ram Krishna Pandey

In this paper we investigate a problem about certain walks in the ring of Gaussian integers. Let $n, d$ be two natural numbers. Does there exist a sequence of Gaussian integers $z_j…

math.NT2015

On Newman's phenomenon in higher bases

Sai Teja Somu

A well known result of Newman says that upto a limit, multiples of $3$ with even number of 1's in binary representation always exceed multiples of $3$ with odd number of 1's. The p…

math.NT2015

On Integer sequences in Product sets

Sai Teja Somu

Let $B$ be a finite set of natural numbers or complex numbers. Product set corresponding to $B$ is defined by $B . B := {ab : a, b \in B}$ . In this paper we give an upper bound for longe…

math.NT2015

On the distribution of numbers related to the divisors of $x^{n} - 1$

Sai Teja Somu

Let $n_{1}, \dots, n_{r}$ be any finite sequence of integers and let $S$ be the set of all natural numbers $n$ for which there exists a divisor $d (x) = 1 + \sum_{i = 1}^{d e g (d)} c_{i} x^{i}$ of $x^…

On Sums of Practical Numbers and Polygonal Numbers

Some Results on Zumkeller Numbers

On Some Results on Practical Numbers

On Power Values of Sum of Divisors function in Arithmetic Progressions

On a Generalization of Tupper's Formula for m Colours and n Dimensions

On Some Generalizations to Floor Function Identities of Ramanujan

Additive Complements for a given Asymptotic Density

On rth coefficient of divisors of xn−1

On the coefficients of divisors of xn−1

On unavoidable obstructions in Gaussian walks

On Newman's phenomenon in higher bases

On Integer sequences in Product sets

On the distribution of numbers related to the divisors of xn−1

On a Generalization of Tupper's Formula for $m$ Colours and $n$ Dimensions

On $r t h$ coefficient of divisors of $x^{n} - 1$

On the coefficients of divisors of $x^{n} - 1$

On the distribution of numbers related to the divisors of $x^{n} - 1$