12 citations · 98 across the 59 of their papers we have counts for
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On 2-powerfully Perfect Numbers in Three Quadratic Rings
Colin Defant
Using an extension of the abundancy index to imaginary quadratic rings with unique factorization, we define what we call -powerfully perfect numbers in these rings. This definit…
Unitary Multiperfect Numbers in Certain Quadratic Rings
Colin Defant
A unitary divisor of a positive integer is a positive divisor of that is relatively prime to . For any integer , the function is…
On Schemmel Nontotient Numbers
Colin Defant
For each positive integer , let denote the Schemmel totient function, a multiplicative arithmetic function defined by \[S_r(p^α)=\begin{cases} 0, & \mbox{if } p\l…
On Sparsely Schemmel Totient Numbers
Colin Defant
For each positive integer , let denote the Schemmel totient function, a multiplicative arithmetic function defined by \[S_r(p^α)=\begin{cases} 0, & \mbox{if } p\l…
An Anti-Ramsey Problem Concerning Complete Bipartite Graphs
Stephan Cho, Jay Cummings, Colin Defant +1
We consider quadruples of positive integers with and such that any proper edge-coloring of the complete bipartite graph contains a rainbow…
Unitary Cayley Graphs of Dedekind Domain Quotients
Colin Defant
If is a commutative ring with unity, then the unitary Cayley graph of , denoted , is defined to be the graph whose vertex set is and whose edge set is $\{\{a,b\}\co…