# Let \$p_k\$ be the \$k\$-th prime number, and let \$a_n= prodlimits_{k=1}^{n}p_k\$..

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