FYI, the name Sempervivum braunii comes from the earlier part of the 1800s, a time when taxonomy was in its infancy, and should be abandoned. According to the Catalog of Life (the resource that the NGA databases defer to), it lists no less than Sempervivum "braunii" having 5 synonyms, which are:
S. braunii Arcangeli (synonym for S. grandiflorum Haw.)
S. braunii Facchinetti (synonym for S. rupicola A. Kerner)
S. braunii Funk ex Koch (synonym for S. montanum subsp. stiriacum (Wettst. ex Hayek) Hayek
S. braunii Ledeb. (synonym for S. pumilum Bieb.)
S. braunii Maly (synonym for S. pittonii Schott, Nyman & Kotschy)
Therefor, there should be no database entry for Sempervivum braunii, as it's not a valid species. Similarly, the name Sempervivum brownii is not one that was ever published, and is most likely a spelling corruption of braunii, and is also not a valid taxon, it only exists in nurseries that hold on to these abandoned or corrupted names. There are hundreds if not thousands of valid species and cultivars to capture our attention and imagination.