P. Pongsriiam

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20172023

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math.NT2023

Directed graphs of integers with arcs determined by an arithmetic function

Phakhinkon Napp Phunphayap, Passawan Noppakaew, Prapanpong Pongsriiam

We introduce a new arc in directed graphs of integers. Among other things, we determine the positive integers that have arcs to all except a finite number of positive integers. We…

math.NT2021

Sums of divisors on arithmetic progressions

Prapanpong Pongsriiam

For each $s \in R$ and $n \in N$ , let $σ_{s} (n) = \sum_{d ∣ n} d^{s}$ . In this article, we give a comparison between $σ_{s} (an + b)$ and $σ_{s} (c n + d)$ where $a$ , $b$ , $c$ , $d$ …

math.NT2020

On Exactly $3$ -Deficient-Perfect Numbers

Saralee Aursukaree, Prapanpong Pongsriiam

Let $n$ and $k$ be positive integers and $σ (n)$ the sum of all positive divisors of $n$ . We call $n$ an exactly $k$ -deficient-perfect number with deficient divisors $d_1, d_2, \ldo…

math.NT2019

Explicit Formulas for the p-adic Valuations of Fibonomial Coefficients II

Phakhinkon Phunphayap, Prapanpong Pongsriiam

In this article, we give explicit formulas for the $p$ -adic valuations of the Fibonomial coefficients $(n p ^{a} n)_{F}$ for all primes $p$ and positive integers $a$ and $n$ . Th…

math.NT2017

The general case on the order of appearance of product of consecutive Fibonacci and Lucas numbers

Narissara Khaochim, Prapanpong Pongsriiam

Let $F_{n}$ and $L_{n}$ be the $n$ th Fibonacci and Lucas number, respectively. For each positive integer $m$ , the order of appearance of $m$ in the Fibonacci sequence, denoted by $z(…