511,768

2³ × 17 × 53 × 71

Starting at 511,768, the Collatz iteration reaches 1 after 58 steps. The first transition is 255884; the starting value is even with 32 positive divisors.

Prime Factor Structure

Factorization String 2^3 × 17 × 53 × 71

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 32

Divisor Sum (σ) 1,049,760

Proper Divisor Sum 537,992

Digit Sum / Digital Root 28 (Root: 1)

Adjacent Primes #511757 ← → #511787

Radix Representation

Decimal	511768
Binary	1111100111100011000 (19 bits)
Octal	0o1747430
Hexadecimal	0x7CF18

Divisor Catalog (32)

1 2 4 8 17 34 53 68 71 106 136 142 212 284 424 568 901 1,207 1,802 2,414 3,604 3,763 4,828 7,208 7,526 9,656 15,052 30,104 63,971 127,942 255,884 511,768

Collatz Trajectory (58 steps to reach 1)

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

511,768 255,884 127,942 63,971 191,914 95,957 287,872 143,936 71,968 35,984 17,992 8,996 4,498 2,249 6,748 3,374 1,687 5,062 2,531 7,594 3,797 11,392 5,696 2,848 1,424 712 356 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1

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