8,261,091

3² × 113 × 8123

Starting at 8,261,091, the Collatz iteration reaches 1 after 106 steps. The first transition is 24783274; the starting value is odd with 12 positive divisors.

Prime Factor Structure

Factorization String 3^2 × 113 × 8123

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 12

Divisor Sum (σ) 12,039,768

Proper Divisor Sum 3,778,677

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #8261041 ← → #8261107

Radix Representation

Decimal	8261091
Binary	11111100000110111100011 (23 bits)
Octal	0o37406743
Hexadecimal	0x7E0DE3

Divisor Catalog (12)

1 3 9 113 339 1,017 8,123 24,369 73,107 917,899 2,753,697 8,261,091

Collatz Trajectory (106 steps to reach 1)

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

8,261,091 24,783,274 12,391,637 37,174,912 18,587,456 9,293,728 4,646,864 2,323,432 1,161,716 580,858 290,429 871,288 435,644 217,822 108,911 326,734 163,367 490,102 245,051 735,154 367,577 1,102,732 551,366 275,683 827,050 413,525 1,240,576 620,288 310,144 155,072 77,536 38,768 19,384 9,692 4,846 2,423 7,270 3,635 10,906 5,453 16,360 8,180 4,090 2,045 6,136 3,068 1,534 767 2,302 1,151 3,454 1,727 5,182 2,591 7,774 3,887 11,662 5,831 17,494 8,747

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