Divisor Count
number_theory · 36 views
number_theory
What It Is
Divisor count d(n) --- erratic arithmetic function averaging ~ln(n), spikes at highly composite numbers, modulated by prime factorization structure
Interpretation
Standard analysis sees: heavy-tailed; right-skewed; anti-correlated (alternating); anti-persistent; blue spectrum (high-frequency power). The atlas detects no named structure beyond this.
What standard analysis sees
tail heaviness0.93
asymmetry0.96
occupancy0.18
short-range corr0.13
long-range memory0.09
spectral colour0.89
periodicity0.71
complexity0.73
time-irreversibility0.42
volatility clustering0.31
multifractality0.45
dimensionality0.50
nonstationarity0.21
What the atlas adds
Nothing beyond the standard reading — this source’s structure is already captured by standard features; the atlas adds no named residual.
Composition
dtypefloat64
range[2, 180]
unique values51 / 16384
mean ± std14.1 ± 15.2
Render Gallery
Native > phase_plotraw
Native > timeseriesraw
Native > triple_latticeraw
Boltzmann > lag_map
Boltzmann > spin_grid
Cayley > default
Chladni > plate_bottom
Chladni > plate_top
_(centered)/signed_log_z/Divisor_Count.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Divisor_Count.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/Divisor_Count.png)
Inflation (Substitution) > barcode
/d_curve/Divisor_Count.png)
Inflation (Substitution) > d_curve
Information Theory > default
Julia Set > escape_histogram
Klein Bottle > default
Laplacian > default
Logarithmic Spiral > default
Möbius-S³ > mobius_cylinder
Möbius-S³ > s2_base_map
Ordinal Partition > default
/phi_spectrum/Divisor_Count.png)
Penrose (Quasicrystal) > phi_spectrum
Persistent Homology > barcode
Persistent Homology > h1_diagram
Predictability > default
Recurrence Quantification > default
Spectral Analysis > default
Spectral Graph > default
Spirograph > mode_spectrum
Spirograph > phasor_trajectory
Symplectic > flux_grid
Symplectic > phase_space
/default/Divisor_Count.png)
Ulam Spiral (Sacks) > default
/default/Divisor_Count.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| Prime Gaps | 3.91 | |
| Aliquot Orbit Lengths | 3.94 | |
| Collatz Flights | 4.29 |
Which Geometries Light Up
2-adic › 2-adic:valuation_transition_predictability | rank 295/298 | 0.3507 |
Zipf–Mandelbrot (16-bit) › Zipf–Mandelbrot (16-bit):zipf_r_squared | rank 4/298 | 0.9877 |
← / → within domain · ⇧← / ⇧→ alphabetical · ⇧← / ⇧→ inside an open render = same view across sources