511,776

2⁵ × 3² × 1777

Starting at 511,776, the Collatz iteration reaches 1 after 195 steps. The first transition is 255888; the starting value is even with 36 positive divisors.

Prime Factor Structure

Factorization String 2^5 × 3^2 × 1777

Distinct Prime Factors 3

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 36

Divisor Sum (σ) 1,456,182

Proper Divisor Sum 944,406

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #511757 ← → #511787

Radix Representation

Decimal	511776
Binary	1111100111100100000 (19 bits)
Octal	0o1747440
Hexadecimal	0x7CF20

Divisor Catalog (36)

1 2 3 4 6 8 9 12 16 18 24 32 36 48 72 96 144 288 1,777 3,554 5,331 7,108 10,662 14,216 15,993 21,324 28,432 31,986 42,648 56,864 63,972 85,296 127,944 170,592 255,888 511,776

Collatz Trajectory (195 steps to reach 1)

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

511,776 255,888 127,944 63,972 31,986 15,993 47,980 23,990 11,995 35,986 17,993 53,980 26,990 13,495 40,486 20,243 60,730 30,365 91,096 45,548 22,774 11,387 34,162 17,081 51,244 25,622 12,811 38,434 19,217 57,652 28,826 14,413 43,240 21,620 10,810 5,405 16,216 8,108 4,054 2,027 6,082 3,041 9,124 4,562 2,281 6,844 3,422 1,711 5,134 2,567 7,702 3,851 11,554 5,777 17,332 8,666 4,333 13,000 6,500 3,250

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