Many real-world scenarios for massive machine-type communication involve sensors monitoring a physical phenomenon. As a consequence, the activity pattern of these sensors will be correlated. In this letter, we study how the correlation of user activities can be exploited to improve detection performance in grant-free random access systems where the users transmit pilot-hopping sequences and the detection is performed based on the received energy. We show that we can expect considerable performance gains by adding regularizers, which take the activity correlation into account, to the non-negative least squares, which has been shown to work well for independent user activity.