M000003535
$$\pi=-4\arctan\left(\frac{1}{3}\right)+24\arctan\left(\frac{1}{5}\right)-8\arctan\left(\frac{1}{7}\right)+12\arctan\left(\frac{1}{12}\right)+24\arctan\left(\frac{1}{21}\right)-24\arctan\left(\frac{1}{34}\right)-24\arctan\left(\frac{1}{55}\right)-12\arctan\left(\frac{1}{70}\right)$$