Based on the community answer, the lens shown appears to be a Pentax K-mount version. If so, it will not mount directly on a Nikon D610. You would need an adapter to use it.

With older third-party Vivitar lenses, the exact mount can vary by version, so the key step is confirming the mount before buying anything. If it is Pentax K, direct fit on Nikon F is not possible without an adapter. Using adapted vintage lenses may also mean manual focus and other limitations depending on the adapter.