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Ratio Atlas
Atlas › Integer Profiles › Node 82,800
82,800
24 × 32 × 52 × 23
Abundant Even Composite

Prime Factor Structure

Factorization String 2^4 × 3^2 × 5^2 × 23
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 90
Divisor Sum (σ) 299,832
Proper Divisor Sum 217,032
Digit Sum / Digital Root 18 (Root: 9)
Adjacent Primes #82799 ← → #82811

Radix Representation

Decimal 82800
Binary 10100001101110000 (17 bits)
Octal 0o241560
Hexadecimal 0x14370

Divisor Catalog (60 of 90)

1 2 3 4 5 6 8 9 10 12 15 16 18 20 23 24 25 30 36 40 45 46 48 50 60 69 72 75 80 90 92 100 115 120 138 144 150 180 184 200 207 225 230 240 276 300 345 360 368 400 414 450 460 552 575 600 690 720 828 900

Collatz Trajectory (151 steps to reach 1)

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

82,800 41,400 20,700 10,350 5,175 15,526 7,763 23,290 11,645 34,936 17,468 8,734 4,367 13,102 6,551 19,654 9,827 29,482 14,741 44,224 22,112 11,056 5,528 2,764 1,382 691 2,074 1,037 3,112 1,556 778 389 1,168 584 292 146 73 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91

Active Feeder Network

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

Feeder #7,737,779 Feeder #685,881 Feeder #2,871,188 Feeder #906,051 Feeder #1,285,993 Feeder #7,584,379 Feeder #4,761,186 Feeder #626,174
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