82,269

3³ × 11 × 277

Starting at 82,269, the Collatz iteration reaches 1 after 89 steps. The first transition is 246808; the starting value is odd with 16 positive divisors.

Prime Factor Structure

Factorization String 3^3 × 11 × 277

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 16

Divisor Sum (σ) 133,440

Proper Divisor Sum 51,171

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #82267 ← → #82279

Radix Representation

Decimal	82269
Binary	10100000101011101 (17 bits)
Octal	0o240535
Hexadecimal	0x1415D

Divisor Catalog (16)

1 3 9 11 27 33 99 277 297 831 2,493 3,047 7,479 9,141 27,423 82,269

Collatz Trajectory (89 steps to reach 1)

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

82,269 246,808 123,404 61,702 30,851 92,554 46,277 138,832 69,416 34,708 17,354 8,677 26,032 13,016 6,508 3,254 1,627 4,882 2,441 7,324 3,662 1,831 5,494 2,747 8,242 4,121 12,364 6,182 3,091 9,274 4,637 13,912 6,956 3,478 1,739 5,218 2,609 7,828 3,914 1,957 5,872 2,936 1,468 734 367 1,102 551 1,654 827 2,482 1,241 3,724 1,862 931 2,794 1,397 4,192 2,096 1,048 524

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