λ
Ratio Atlas
Atlas › Integer Profiles › Node 31,680
31,680
26 × 32 × 5 × 11
Abundant Even Composite

Prime Factor Structure

Factorization String 2^6 × 3^2 × 5 × 11
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 84
Divisor Sum (σ) 118,872
Proper Divisor Sum 87,192
Digit Sum / Digital Root 18 (Root: 9)
Adjacent Primes #31667 ← → #31687

Radix Representation

Decimal 31680
Binary 111101111000000 (15 bits)
Octal 0o75700
Hexadecimal 0x7BC0

Divisor Catalog (60 of 84)

1 2 3 4 5 6 8 9 10 11 12 15 16 18 20 22 24 30 32 33 36 40 44 45 48 55 60 64 66 72 80 88 90 96 99 110 120 132 144 160 165 176 180 192 198 220 240 264 288 320 330 352 360 396 440 480 495 528 576 660

Collatz Trajectory (103 steps to reach 1)

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

31,680 15,840 7,920 3,960 1,980 990 495 1,486 743 2,230 1,115 3,346 1,673 5,020 2,510 1,255 3,766 1,883 5,650 2,825 8,476 4,238 2,119 6,358 3,179 9,538 4,769 14,308 7,154 3,577 10,732 5,366 2,683 8,050 4,025 12,076 6,038 3,019 9,058 4,529 13,588 6,794 3,397 10,192 5,096 2,548 1,274 637 1,912 956 478 239 718 359 1,078 539 1,618 809 2,428 1,214

Active Feeder Network

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

Feeder #3,913,373 Feeder #8,365,252 Feeder #6,970,568 Feeder #906,051 Feeder #1,285,993 Feeder #7,584,379 Feeder #4,761,186 Feeder #626,174
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