Carlos Rojas Mena

$τ$-Norm-Perfect and $τ$-Perfect Eisenstein Integers for $τ=ω+2$ and $2$

Using Robert Spira's \cite{D} definitions of complex Mersenne numbers and the complex sum-of-divisors function, we characterize $(ω+2)$-norm-perfect and $(ω+2)$-perfect numbers that are divisble by $ω+2$ and prove the nonexistence of $2$-norm-perfect numbers that are divisible by $2$ in the Eisenstein integers.