We have had two other topics wanting to do a similar thing recently.
They are:
not-sure-where-to-go-hz-question.
and
arduino-nano-reading-an-input-frequency-and-outputting-a-different-frequency.
In the first one, I proposed (and tested) a solution that used an interrupt to measure the incoming frequency, and used timer 1 to generate the output frequency.
The code suffered from the same issue as using tone() does, in that there is a minimum frequency that can be produced.
However it was acceptable for the frequencies that were required in that case.
Timer 1 has a prescaler which I did not use, but that can be used to divide the frequency by 8, 64, 256 or 1024.
Once we hear from pmeckl393 what frequency range and division ratio is required, then I can alter my code to use a more appropriate prescaler value.