820,026

2 × 3² × 45557

Starting at 820,026, the Collatz iteration reaches 1 after 82 steps. The first transition is 410013; the starting value is even with 12 positive divisors.

Prime Factor Structure

Factorization String 2 × 3^2 × 45557

Distinct Prime Factors 3

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 12

Divisor Sum (σ) 1,776,762

Proper Divisor Sum 956,736

Digit Sum / Digital Root 18 (Root: 9)

Adjacent Primes #819991 ← → #820037

Radix Representation

Decimal	820026
Binary	11001000001100111010 (20 bits)
Octal	0o3101472
Hexadecimal	0xC833A

Divisor Catalog (12)

1 2 3 6 9 18 45,557 91,114 136,671 273,342 410,013 820,026

Collatz Trajectory (82 steps to reach 1)

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

820,026 410,013 1,230,040 615,020 307,510 153,755 461,266 230,633 691,900 345,950 172,975 518,926 259,463 778,390 389,195 1,167,586 583,793 1,751,380 875,690 437,845 1,313,536 656,768 328,384 164,192 82,096 41,048 20,524 10,262 5,131 15,394 7,697 23,092 11,546 5,773 17,320 8,660 4,330 2,165 6,496 3,248 1,624 812 406 203 610 305 916 458 229 688 344 172 86 43 130 65 196 98 49 148

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