Denote by $A_n$ the least common multiple of the integers from 1 to n, prove that $\displaystyle\sum_{n=1}^{\infty} \dfrac{f(n)}{A_n}$ is irrational, where $f(x)$ is a polynomial with integer coefficients. This problem was introduced by Erdős and published on Pi Mu Epsilon Journal Problems without a solution!
I have difficulty finishing it.