6 citations · 15 across the 8 of their papers we have counts for
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On the genus of a quotient of a numerical semigroup
Ayomikun Adeniran, Steve Butler, Colin Defant +6
We find a relation between the genus of a quotient of a numerical semigroup and the genus of itself. We use this identity to compute the genus of a quotient of when …
On Ranges of Variants of the Divisor Functions that are Dense
Colin Defant
For a real number , let be the multiplicative arithmetic function defined by for all primes and positive integers . W…
On the Density of Ranges of Generalized Divisor Functions
Colin Defant
The range of the divisor function is dense in the interval . However, the range of the function is not dense in the interval $\displaystyle{\left[1,\f…
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…
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…
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 -powerfully -perfect numbers in thes…