There is a method for finding all the prime numbers up to $n>0$ called the Sieve of Eratosthenes, which you can read about on Wikipedia. The sieve can be modified it so that it counts the number factors of all the numbers from $1$ to $n$ by doing the following:

Make a list of the numbers from $1$ to $n,$ and set the number of factors of each to $0.$

Starting at $1,$ add one to the number of factors of every number up to $n.$

Starting at $2,$ add one to the number of factors of every second number up to $n.$

Starting at $3,$ add one to the number of factors of every third number up to $n.$

Starting at $4,$ add one to the number of factors of every fourth number up to $n.$

$30$

$...$

Starting at $n,$ add one to the number of factors of every $n^{th}$ number up to $n.$

Note, the last step only increments one number.

Write a program that reads in $n,$ checks it is a sensible value and then prints out all the numbers from $1$ to $n$ along with how many factors it has. It should print a star beside any number that has the more factors than any smaller number $($e$.$g$.1,2,4,6$ and $12$ should each get a star because they are the smallest numbers to have $1,2,3,4$ and $6$ factors$).$

Hint: You can assume $n1000,$ but you should make it easy to increase this limit$.$

$1$

P$.$T$.$O$.$