we can write $ n =\prod_{k=1}^{g}q_k \prod_{i = 1}^{h}p_i^{a_i}$ i)$ p_i,q_k$ are primes ii) $ a_i>1$ iii) $ q_1<q_2<...<q_g$ we take $ d = \prod_{i = 1}^{h}p_i^{b_i}$ where $ b_i = [a_i/2]: \ (2b_i\le a_i)$ if $ g\ge 2$ we take $ d'=\prod_{k=1}^{[q/2]}q_k$ and $ m=dd'\le \sqrt{n}$ and $ d^3(m) =2^{3[g/2]} \prod_{i = 1}^{h}(b_i + 1)^3\ge 2^g\prod_{i = 1}^{h}(a_i + 1) = d(n)$