In many online social networking platforms, the participation of an individual is motivated by the participation of others. If an individual chooses to leave a platform, this may produce a cascade in which that person’s friends then choose to leave, causing their friends to leave, and so on. In some cases, it may be possible to incentivize key individuals to stay active within the network, thus preventing such a cascade. This problem is modeled using the anchored k-core of a network, which, for a network G and set of anchor nodes A, is the maximal subgraph of G in which every node has a total of at least k neighbors between the subgraph and anchors. In this work, we propose Residual Core Maximization (RCM), a novel algorithm for finding b anchor nodes so that the size of the anchored k-core is maximized. We perform a comprehensive experimental evaluation on numerous real-world networks and compare RCM to various baselines. We observe that RCM is more effective and efficient than the state-of-the-art methods: on average, RCM produces anchored k-cores that are 1.65 times larger than those produced by the baseline algorithm, and is approximately 500 times faster on average.