KMO 2016 Problem 7

Let $N=2^a p_1^{b_1} p_2^{b_2} \ldots p_k^{b_k}$ . Prove that there are $(b_1+1)(b_2+1)\ldots(b_k+1)$ number of $n$ s which satisfies these two conditions. $\frac{n(n+1)}{2}\le N$ , $N-\frac{n(n+1)}{2}$ is divided by $n$ .