On a certain class of arithmetic functions

Oller-Marcén, Antonio M.. "On a certain class of arithmetic functions." Mathematica Bohemica 142.1 (2017): 21-25. <http://eudml.org/doc/287924>.

@article{Oller2017,
abstract = {A homothetic arithmetic function of ratio $K$ is a function $f\colon \mathbb \{N\}\rightarrow R$ such that $f(Kn)=f(n)$ for every $n\in \mathbb \{N\}$. Periodic arithmetic funtions are always homothetic, while the converse is not true in general. In this paper we study homothetic and periodic arithmetic functions. In particular we give an upper bound for the number of elements of $f(\mathbb \{N\})$ in terms of the period and the ratio of $f$.},
author = {Oller-Marcén, Antonio M.},
journal = {Mathematica Bohemica},
keywords = {arithmetic function; periodic function; homothetic function},
language = {eng},
number = {1},
pages = {21-25},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On a certain class of arithmetic functions},
url = {http://eudml.org/doc/287924},
volume = {142},
year = {2017},
}

TY - JOUR
AU - Oller-Marcén, Antonio M.
TI - On a certain class of arithmetic functions
JO - Mathematica Bohemica
PY - 2017
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 142
IS - 1
SP - 21
EP - 25
AB - A homothetic arithmetic function of ratio $K$ is a function $f\colon \mathbb {N}\rightarrow R$ such that $f(Kn)=f(n)$ for every $n\in \mathbb {N}$. Periodic arithmetic funtions are always homothetic, while the converse is not true in general. In this paper we study homothetic and periodic arithmetic functions. In particular we give an upper bound for the number of elements of $f(\mathbb {N})$ in terms of the period and the ratio of $f$.
LA - eng
KW - arithmetic function; periodic function; homothetic function
UR - http://eudml.org/doc/287924
ER -