Douglas E. Iannucci

activity

20152021

most citedOn sums of the small divisors of a natural number

3 citations · 3 across the 5 of their papers we have counts for

collaborators

5 papers

math.NT2021

Game values of arithmetic functions

Douglas E. Iannucci, Urban Larsson

Arithmetic functions in Number Theory meet the Sprague-Grundy function from Combinatorial Game Theory. We study a variety of 2-player games induced by standard arithmetic functions…

math.GM2020

On compositions of natural numbers

Douglas E. Iannucci

In this expository note, we introduce the reader to compositions of a natural number, e.g., $2 + 1 + 2 + 1 + 7 + 1$ is a composition of 14, and $1 + 2$ and $2 + 1$ are two different compositions…

math.NT2019★ 3 cited

On sums of the small divisors of a natural number

Douglas E. Iannucci

We consider the positive divisors of a natural number that do not exceed its square root, to which we refer as the {\it small divisors\/} of the natural number. We determine the as…

math.NT2019

On duplicate representations as $2^{x} + 3^{y}$ for nonnegative integers $x$ and $y$

Douglas Edward Iannucci

We prove a conjecture posted in the Online Encyclopedia of Integer Sequences, namely that there are exactly five positive integers that can be written in more than one way as the s…

math.NT2015

On primitive weird numbers of the form $2^{k} pq$

Douglas E. Iannucci

We say a natural number~ $n$ is abundant if $σ (n) > 2 n$ , where $σ (n)$ denotes the sum of the divisors of~ $n$ . The aliquot parts of~ $n$ are those divisors less than~ $n$ , and we say tha…

Game values of arithmetic functions

On compositions of natural numbers

On sums of the small divisors of a natural number

On duplicate representations as 2x+3y for nonnegative integers x and y

On primitive weird numbers of the form 2kpq

On duplicate representations as $2^{x} + 3^{y}$ for nonnegative integers $x$ and $y$

On primitive weird numbers of the form $2^{k} pq$