Colin Defant

most citedOn the Density of Ranges of Generalized Divisor Functions

6 citations · 13 across the 4 of their papers we have counts for

collaborators

6 papers

math.NT2015

On Ranges of Variants of the Divisor Functions that are Dense

Colin Defant

For a real number $t$ , let $s_{t}$ be the multiplicative arithmetic function defined by $s_{t} (p^{α}) = j = 0 \sum α (- p^{t})^{j}$ for all primes $p$ and positive integers $α$ . W…

math.CO2015

Upper Bounds for Stern's Diatomic Sequence and Related Sequences

Colin Defant

Let $(s_{2} (n))_{n = 0}^{\infty}$ denote Stern's diatomic sequence. For $n \geq 2$ , we may view $s_{2} (n)$ as the number of partitions of $n - 1$ into powers of $2$ with each part occurring a…

math.NT2015★ 6 cited

On the Density of Ranges of Generalized Divisor Functions

Colin Defant

The range of the divisor function $σ_{- 1}$ is dense in the interval $[1, \infty)$ . However, the range of the function $σ_{- 2}$ is not dense in the interval $\displaystyle{\left[1,\f…

math.NT2015★ 2 cited

On Arithmetic Functions Related to Iterates of the Schemmel Totient Functions

Colin Defant

We begin by introducing an interesting class of functions, known as the Schemmel totient functions, that generalizes the Euler totient function. For each Schemmel totient function…

math.NT2015★ 4 cited

An Extension of the Abundancy Index to Certain Quadratic Rings

Colin Defant

We begin by introducing an extension of the traditional abundancy index to imaginary quadratic rings with unique factorization. After showing that many of the properties of the tra…

math.NT2015★ 1 cited

Multiperfect Numbers in Certain Quadratic Rings

Colin Defant

Using an extension of the abundancy index to imaginary quadratic rings that are unique factorization domains, we investigate what we call $n$ -powerfully $t$ -perfect numbers in thes…