E096: Record-holders for τ(n)

E096 hero

E096: Record-holders for τ(n)

Tags: number-theory, quantitative-exploration, visualization, divisor-function, arithmetic-functions

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

  • Track the running maxima of τ(n) up to N and visualize the growth of record values.

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_tau_records.png

  • params.json

  • report.md

Notes

  • Number of record-holders found: 33

  • Last 10 record-holders (n, τ(n)): [(25200, 90), (27720, 96), (45360, 100), (50400, 108), (55440, 120), (83160, 128), (110880, 144), (166320, 160), (221760, 168), (277200, 180)]

  • Record-holders are built from small primes with nonincreasing exponents (highly composite flavor).

params.json (snapshot)
{
  "max_points": 150,
  "n_max": 300000
}

References

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

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