M000003561
$$\pi=4\arctan\left(\frac{1}{2}\right)+12\arctan\left(\frac{1}{3}\right)-8\arctan\left(\frac{1}{5}\right)+4\arctan\left(\frac{1}{13}\right)-12\arctan\left(\frac{1}{15}\right)-8\arctan\left(\frac{1}{21}\right)-12\arctan\left(\frac{1}{81}\right)+12\arctan\left(\frac{1}{467}\right)$$