DIVISORS OF THE PRODUCTS OF CONSECUTIVE INTEGERS

In this Paper, We look at 3 Simple function L assigning to an integer n the smallest positive integer n such that any product of n consecutive numbers is divisible by n. Investigated are the interesting properties of the function. The function L(n) is completely determined by L(p$\^$k/), where p$\^$k/ is a factor of n, and satisfies L(m$.$n) $\leq$ L(m)+L(n), where the equality holds for infinitely many cases.