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Ratio Atlas
Atlas › Integer Profiles › Node 78,000
78,000
24 × 3 × 53 × 13
Abundant Even Composite

Prime Factor Structure

Factorization String 2^4 × 3 × 5^3 × 13
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 80
Divisor Sum (σ) 270,816
Proper Divisor Sum 192,816
Digit Sum / Digital Root 15 (Root: 6)
Adjacent Primes #77999 ← → #78007

Radix Representation

Decimal 78000
Binary 10011000010110000 (17 bits)
Octal 0o230260
Hexadecimal 0x130B0

Divisor Catalog (60 of 80)

1 2 3 4 5 6 8 10 12 13 15 16 20 24 25 26 30 39 40 48 50 52 60 65 75 78 80 100 104 120 125 130 150 156 195 200 208 240 250 260 300 312 325 375 390 400 500 520 600 624 650 750 780 975 1,000 1,040 1,200 1,300 1,500 1,560

Collatz Trajectory (125 steps to reach 1)

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

78,000 39,000 19,500 9,750 4,875 14,626 7,313 21,940 10,970 5,485 16,456 8,228 4,114 2,057 6,172 3,086 1,543 4,630 2,315 6,946 3,473 10,420 5,210 2,605 7,816 3,908 1,954 977 2,932 1,466 733 2,200 1,100 550 275 826 413 1,240 620 310 155 466 233 700 350 175 526 263 790 395 1,186 593 1,780 890 445 1,336 668 334 167 502

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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