I realized that attachments are stripped out. I had transcribed the column into TeX. Here it is: Sol Golomb's column in the December 2011 of the IT Newsletter: The Sequence $n^3-n$ For every $n>1$ each term of the sequence $[n^3-n]$ is the product of the three consecutive positive integers, $n-1,n,$ and $n+1$. the sequence begins $[6,24,60,12-,240,336,\dots]$. Here are some questions about this sequence. 1) For which values of $n>1$ is $n^3-n=k!$ for some integer $k$? 2) For $n>3$, prove that $n^3-n$ must have at least three different prime factors. 3) What are all the values of $n>1$ for which $n^3-n$ has (only) three different prime factors? (The same prime factor is allowed to occur more than once in $n^3-n$). 4) What three different conditions on one of the $(n-1,n,n+1)$ may make it possible for $n^3-n$ to have (only) four different prime factors? (The same prime factor is allowed to occur more than once). The number of cases of each type appears to be infinite, but thsi cannot be currently proved. 5) Try to list all $n, 3 < n < 10^6$, for which $n^3-n$ has exactly four different prime factors. The same prime factor is allowed to occur more than once. (A computer program may be used, but the number of examples is not huge).

From here on, we consider only those $n > 1$ for which $n^3- n$ is {\em square-free}; i.e. that each prime factor of $n^3-n$ occurs only to the first power.

6) Which two prime numbers must divide $n^3-n$ for every $n>1$? What can you say about which factors, among $n-1,n$ and $n+1$, each of these two prime will divide? 7) Asymptotically, what fraction of integers $n, 1< n \le x$, give square-free values of $n^3-n$? (Give an infinite product expression and a numerical value). 8) Show that if $n^3-n$ is square-free, it can have $k < 5$ distinct prime factors only finitely many times. 9) List all values of $n>1$ for which $n^3-n$ is square-free with $k$ distinct prime factors, $1 < k < 5$. 10) List the first three occurrences of square-free $n^3-n$ having exactly $k$ distinct prime factors for each $k, 5 \le k \le 10$. (The smallest cases for $k=5,6,8,$ and $9$ are remarkable for the number of different small prime factors found among three consecutive integers).