Consider a natural number, say $n$. 


Find the first number which is greater than or equal to $n$ and is a multiple of $n-1$.


Again find a number which is greater than or equal to this number and is a multiple of $n-2$.


Do this iteratively until a multiple of $2$ occurs and call the last number $x$. 


(More formally: define numbers $a\_1, a\_2, \ldots, a\_n$ where $a\_1 = n$ and $a\_{k+1}$ is the least number greater than or equal to $a\_k$ that is a multiple of $n-k$. Put $x = a\_n$.) 


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I want to prove that $x$ is asymptotic to $n^2/\pi$.


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It's easy to see that $x$ is greater than $n^2/4$ because the first half of procedure can be determined and it achieves $n^2/4$ but the proof must be much harder...


Can somebody help me?


Thanks...



why this procedure grows asymptotically to $n^2/\pi$
This is proved by [Kevin Brown](http://www.mathpages.com/home/kmath001/kmath001.htm). The numbers are tabulated, and many links and references given, at the [Online Encyclopedia of Integer Sequences](http://oeis.org/A002491). 


