In the field of chemical graph theory, a Wiener (topological) index is a type of a molecular descriptor that is calculated based on the molecular graph of alkanes. It gives the sum of geodesic distances (or shortest paths) between all pairs of vertices of the graph. We found and prove the Wiener indices of some Brooms, which are Caterpillars, giving several unknown sequences that are now added to the collection of the largest Online Encyclopedia of Integer Sequences.