E097: σ(n)/n landscape: deficient, perfect, abundant

E097 hero

E097: σ(n)/n landscape: deficient, perfect, abundant

Tags: number-theory, quantitative-exploration, visualization, sigma, perfect, classification

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

  • Visualize σ(n)/n and classify integers using σ(n) compared to 2n.

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).

Artifacts

  • figures/fig_01_sigma_over_n_scatter.png

  • params.json

  • report.md

Notes

  • Fraction abundant (σ(n)>2n) up to N: 0.2474

  • Number of perfect numbers detected up to N: 7

  • First perfect numbers in range (if any): [6, 28, 496, 8128, 65536, 130304, 131072]

params.json (snapshot)
{
  "n_max": 200000,
  "stride": 20
}

References

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

  • See the perfect-numbers and divisor-functions background pages in docs/background/.