Dicey situation

I have a bias 6-sided dice (with faces 1, 2, 3, 4, 5, 6) such that for integer $1\leq k \leq 6$ , the probability of rolling a $k$ is inversely proportional to $k$ itself. That is, $P(k) \propto \dfrac1k$ . If the variance of the probability distribution of this dice can be expressed as $\dfrac{V}{7^4}$ , find $V$ .