Let $p_k$ be

the $k$-th prime number, and let $a_n= prodlimits_{k=1}^{n}p_k$. Prove that for $ninmathbb{N}$ every positive integer

less than $a_n$ can be expressed as a sum of at most $2k$ distinct divisors of $a_n$.

Please give some hint for this problem. A small hint will be appreciated. I tried by listing $a_n$ but could not proceed more