Clustering is a fundamental problem setting with applications in many different areas. For a given set of points in a metric space and an integer k, we seek to partition the given points into k clusters. For each computed cluster, one typically defines one point as the center of the cluster. A natural objective is to minimize the sum of the cluster center's radii, where we assign the smallest radius r to each center such that each point in the cluster is at a distance of at most r from the center. The best-known polynomial time approximation ratio for this problem is 3.389. In the setting with outliers, i.e., we are given an integer m and allow up to m points that are not in any cluster, the best-known approximation factor is 12.365.