3 citations · 5 across the 11 of their papers we have counts for
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An Arithmetic Function Arising from the Dedekind Function
Colin Defant
We define to be the multiplicative arithemtic function that satisfies \[\overlineψ(p^α)=\begin{cases} p^{α-1}(p+1), & \mbox{if } p\neq 2; \\ p^{α-1}, & \mbox{if } p=2…
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…