2³ × 3⁴ × 7 × 17

Prime Factor Structure

Factorization String 2^3 × 3^4 × 7 × 17

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 80

Divisor Sum (σ) 261,360

Proper Divisor Sum 184,248

Digit Sum / Digital Root 18 (Root: 9)

Adjacent Primes #77101 ← → #77137

Radix Representation

Decimal	77112
Binary	10010110100111000 (17 bits)
Octal	0o226470
Hexadecimal	0x12D38

Divisor Catalog (60 of 80)

1 2 3 4 6 7 8 9 12 14 17 18 21 24 27 28 34 36 42 51 54 56 63 68 72 81 84 102 108 119 126 136 153 162 168 189 204 216 238 252 306 324 357 378 408 459 476 504 567 612 648 714 756 918 952 1,071 1,134 1,224 1,377 1,428

Collatz Trajectory (138 steps to reach 1)

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

77,112 38,556 19,278 9,639 28,918 14,459 43,378 21,689 65,068 32,534 16,267 48,802 24,401 73,204 36,602 18,301 54,904 27,452 13,726 6,863 20,590 10,295 30,886 15,443 46,330 23,165 69,496 34,748 17,374 8,687 26,062 13,031 39,094 19,547 58,642 29,321 87,964 43,982 21,991 65,974 32,987 98,962 49,481 148,444 74,222 37,111 111,334 55,667 167,002 83,501 250,504 125,252 62,626 31,313 93,940 46,970 23,485 70,456 35,228 17,614

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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