Finding a generalized inverse (approximation) for multi-factorials given the number of factorials

[silent nimbus]

I originally asked this question on https://math.stackexchange.com/questions/4676507/finding-a-generalized-inverse-approximation-for-multi-factorials-given-k but it seems I am not going to get any answers or hints or comments at all.

I am trying to find the inverse of:

$$f(n) = \prod_{x=1}^{n}x^{0^{\left|\left(\operatorname{mod}\left(x,k\right)-\operatorname{mod}\left(n,k\right)\right)\right|}}$$

for $k, n \in \mathbb{Z}^+$ (as that is where it is monotonically increasing and has an inverse)

[compact hazel]

Sawbeez

[lean jacinth]

.close