"How many different integers does this give us?" How many unique integers can you get from
$\lceil2012/n\rceil$
where $n$ is a positive integer?
I don't know at all where to begin to approach this problem. I thought it maybe had something to do with which factors the number has or anything like that, but I couldn't find any obvious pattern.

Here is a program that will print 89 like @joriki said!!
class Program
    {

        static void Main(string[] args)
        {
            int n = 1,c=0;
            double prev = 0;
            for (n = 1 ; n <= 2012; n++)
            {
                double curr=Math.Ceiling((double)2012/n);
                if (prev != curr) c++;
                //Console.WriteLine(curr.ToString());
                prev=curr;
            }
            Console.WriteLine(c.ToString());
            Console.Read();
        }
    }

