# E094: ω(n) vs. Ω(n): Erdős–Kac normalization

```{figure} ../_static/experiments/e094_hero.png
:alt: E094 hero
:class: experiment-hero

E094: ω(n) vs. Ω(n): Erdős–Kac normalization
```

**Tags:** `number-theory`, `quantitative-exploration`, `visualization`, `omega`, `arithmetic-functions`, `numerics`

## Highlights

- Focused numeric experiment with a small set of figures.
- Parameters saved to `params.json` for reproducibility.
- Defaults are chosen, so the experiment remains feasible for the CI “slow” suite.

## What is computed

- Compare ω(n) and Ω(n) distributions and their Erdős–Kac normalizations.

## Notes

- This page summarizes the intent; see the generated `report.md` in `out/` for concrete outputs.

## Published run snapshot

If this experiment is included in the docs gallery, include the published snapshot (report + params).

```{include} ../reports/e094.md
:start-after: "<!-- REPORT:BEGIN -->"
:end-before: "<!-- REPORT:END -->"
```

::: {dropdown} params.json (snapshot)
:open:

```{literalinclude} ../params/e094.json
:language: json
```

:::

## References

- See the arithmetic-functions background pages in `docs/background/`.

## Related experiments

- {doc}`e057` (Erdős–Kac in practice)
- {doc}`e095` (E095: Squarefree filter: ω(n)=Ω(n) when μ(n)≠0)
- {doc}`e120` (E120: Liouville λ(n): partial sums and parity)
- {doc}`e052` (Totient ratio landscape)
- {doc}`e053` (Inverse totient multiplicities)