Problem

Source: 48th Austrian Mathematical Olympiad Beginners' Competition(2047)

Tags: combinatorics, number theory



. Anthony denotes in sequence all positive integers which are divisible by $2$. Bertha denotes in sequence all positive integers which are divisible by $3$. Claire denotes in sequence all positive integers which are divisible by $4$. Orderly Dora denotes all numbers written by the other three. Thereby she puts them in order by size and does not repeat a number. What is the $2017th$ number in her list? ¨Proposed by Richard Henner