# Mathematica, 35 bytes

    #//.x_:>Tr[1##&@@@FactorInteger@x]&

[Try it online!][TIO-j8cxcfmk]

(Mathics does not support `Tr`. Use `Tr = Total` in this particular case works)

[TIO-j8cxcfmk]: https://tio.run/##y00sychMLv4fUmQbkl@SmGPNlWb7X1lfX68i3soupCjaUFlZzcHBwS0xuSS/yDOvJDU9tcihIlbtf0BRZl5JtLKOgpKCrp2Cko5CmoNyrJqCvoNCtZGJjoKhoY6CkalB7X8A "Mathics – Try It Online"