The Husqvarna Improved Mauser was first introduced as the 1640 the 1600 and the 1651 names came later. So, the correct "familly" name would be 1640.
1640, 1600 and 1651 are European (Swedish) designation of the barreled action, followed by Standard, Lyx, Special, Helstock, MC etc which are the types of "dressing" or "trim" of the stock, sights, and calibers (for the 1651).
The 4000 / 4100 / 450 and "Lightweight" are the common US / Canada short barreled version of the 1600 series in Europe. This version have a 520mm barrel.
The 4000/4100 a.k.a. Lightweight have checkering at the fore end while most European versions did not. They were also made in calibers not so popular in Sweden (except, maybe the 30-06) means 7X57, .243 Win, .308 Win, 270 Win and 30-06 Sprg.
The 3000 / 3100 are the long version (600mm) which is the 1640 series, which also includes the versions with 560mm barrels (Husky / H-5000).
Check the HVA #### sticky thread for examples of 1640 series.