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Ratio Atlas
Atlas › Integer Profiles › Node 820,800
820,800
26 × 33 × 52 × 19
Abundant Even Composite

Prime Factor Structure

Factorization String 2^6 × 3^3 × 5^2 × 19
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 168
Divisor Sum (σ) 3,149,600
Proper Divisor Sum 2,328,800
Digit Sum / Digital Root 18 (Root: 9)
Adjacent Primes #820793 ← → #820837

Radix Representation

Decimal 820800
Binary 11001000011001000000 (20 bits)
Octal 0o3103100
Hexadecimal 0xC8640

Divisor Catalog (60 of 168)

1 2 3 4 5 6 8 9 10 12 15 16 18 19 20 24 25 27 30 32 36 38 40 45 48 50 54 57 60 64 72 75 76 80 90 95 96 100 108 114 120 135 144 150 152 160 171 180 190 192 200 216 225 228 240 270 285 288 300 304

Collatz Trajectory (56 steps to reach 1)

Iterative sequence n → n/2 (if even) or 3n+1 (if odd):

820,800 410,400 205,200 102,600 51,300 25,650 12,825 38,476 19,238 9,619 28,858 14,429 43,288 21,644 10,822 5,411 16,234 8,117 24,352 12,176 6,088 3,044 1,522 761 2,284 1,142 571 1,714 857 2,572 1,286 643 1,930 965 2,896 1,448 724 362 181 544 272 136 68 34 17 52 26 13 40 20 10 5 16 8 4 2 1

Active Feeder Network

Other feeder batches with open delivery windows. Each feeder keeps its own target batch.

Feeder #6,573,969 Feeder #2,443,427 Feeder #6,845,105 Feeder #906,051 Feeder #1,285,993 Feeder #7,584,379 Feeder #4,761,186 Feeder #626,174
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