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# [Jelly], 7 bytes

    *Ḃ×½ḞµƬ

```
*Ḃ×½ḞµƬ
*Ḃ        input ^ (input % 2)
  ×½      multiply sqrt(input)
    Ḟ     floor
     µƬ   iterate until converged and collect results
```

[Try it online!][TIO-koeu086r]

[Jelly]: https://github.com/DennisMitchell/jelly
[TIO-koeu086r]: https://tio.run/##AS0A0v9qZWxsef//KuG4gsOXwr3huJ7Ctcas/8OH4oKs//9bMiwzLDQsNSw2LDcsOF0 "Jelly – Try It Online"