Nikon D3000 lense compatibility

I have a Nikon D3000. I'm wondering what kind of Vivitar, Sigma, or Tamron lenses that are compatible with my camera?

With your D3000 the lens MUST have a focusing motor built into it in order for it to auto focus.

Sigma lenses with HSM in their description will auto focus on your D3000. A Sigma lens with OS in the description is an Optically Stabilized lens, comparable to a Nikon VR (Vibration Reduction) lens.

Tamron lenses with a Nikon mount have a focusing motor. If a Tamron lens has VC in the description that means its a Vibration Control lens, comparable to a Nikon VR lens.