64,192

2⁶ × 17 × 59

Starting at 64,192, the Collatz iteration reaches 1 after 47 steps. The first transition is 32096; the starting value is even with 28 positive divisors.

Prime Factor Structure

Factorization String 2^6 × 17 × 59

Distinct Prime Factors 3

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 28

Divisor Sum (σ) 137,160

Proper Divisor Sum 72,968

Digit Sum / Digital Root 22 (Root: 4)

Adjacent Primes #64189 ← → #64217

Radix Representation

Decimal	64192
Binary	1111101011000000 (16 bits)
Octal	0o175300
Hexadecimal	0xFAC0

Divisor Catalog (28)

1 2 4 8 16 17 32 34 59 64 68 118 136 236 272 472 544 944 1,003 1,088 1,888 2,006 3,776 4,012 8,024 16,048 32,096 64,192

Collatz Trajectory (47 steps to reach 1)

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

64,192 32,096 16,048 8,024 4,012 2,006 1,003 3,010 1,505 4,516 2,258 1,129 3,388 1,694 847 2,542 1,271 3,814 1,907 5,722 2,861 8,584 4,292 2,146 1,073 3,220 1,610 805 2,416 1,208 604 302 151 454 227 682 341 1,024 512 256 128 64 32 16 8 4 2 1

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