Unitary Multiperfect Numbers in Certain Quadratic Rings

zbMATH Open1397.11148arXiv1412.3105MaRDI QIDQ2960891

Author name not available (Why is that?)

Publication date: 17 February 2017

Abstract: A unitary divisor

c

of a positive integer

n

is a positive divisor of

n

that is relatively prime to

d i s p l a y s t y l e f r a c n c

. For any integer

k

, the function

s i g m a_{k}^{*}

is a multiplicative arithmetic function defined so that

s i g m a_{k}^{*} (n)

is the sum of the

k^{t h}

powers of the unitary divisors of

n

. We provide analogues of the functions

s i g m a_{k}^{*}

in imaginary quadratic rings that are unique factorization domains. We then explore properties of what we call

n

-powerfully unitarily

t

-perfect numbers, analogues of the unitary multiperfect numbers that have been defined and studied in the integers. We end with a list of several opportunities for further research.

Full work available at URL: https://arxiv.org/abs/1412.3105

zbMATH Keywords

No records found.

Mathematics Subject Classification ID

No records found.

This page was built for publication: Unitary Multiperfect Numbers in Certain Quadratic Rings

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q2960891)