# E098: Maximizers of σ(n)/n^α across α

```{figure} ../_static/experiments/e098_hero.png
:alt: E098 hero
:class: experiment-hero

E098: Maximizers of σ(n)/n^α across α
```

**Tags:** `number-theory`, `quantitative-exploration`, `visualization`, `sigma`, `optimization`

## 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

- For α on a grid, find n≤N maximizing σ(n)/n^α and show regime changes.

## 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/e098.md
:start-after: "<!-- REPORT:BEGIN -->"
:end-before: "<!-- REPORT:END -->"
```

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

```{literalinclude} ../params/e098.json
:language: json
```

:::

## References

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

## Related experiments

- {doc}`e004` (Computing $\sigma(n)$ at Scale — Sieve vs. Factorization)
- {doc}`e059` (Abundancy index landscape)
- {doc}`e097` (E097: σ(n)/n landscape: deficient, perfect, abundant)
- {doc}`e078` (Max partial sums across characters.)
- {doc}`e002` (Even Perfect Numbers — Generator and Growth)