7,382,205

3³ × 5 × 149 × 367

Starting at 7,382,205, the Collatz iteration reaches 1 after 204 steps. The first transition is 22146616; the starting value is odd with 32 positive divisors.

Prime Factor Structure

Factorization String 3^3 × 5 × 149 × 367

Distinct Prime Factors 4

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 32

Divisor Sum (σ) 13,248,000

Proper Divisor Sum 5,865,795

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #7382201 ← → #7382209

Radix Representation

Decimal	7382205
Binary	11100001010010010111101 (23 bits)
Octal	0o34122275
Hexadecimal	0x70A4BD

Divisor Catalog (32)

1 3 5 9 15 27 45 135 149 367 447 745 1,101 1,341 1,835 2,235 3,303 4,023 5,505 6,705 9,909 16,515 20,115 49,545 54,683 164,049 273,415 492,147 820,245 1,476,441 2,460,735 7,382,205

Collatz Trajectory (204 steps to reach 1)

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

7,382,205 22,146,616 11,073,308 5,536,654 2,768,327 8,304,982 4,152,491 12,457,474 6,228,737 18,686,212 9,343,106 4,671,553 14,014,660 7,007,330 3,503,665 10,510,996 5,255,498 2,627,749 7,883,248 3,941,624 1,970,812 985,406 492,703 1,478,110 739,055 2,217,166 1,108,583 3,325,750 1,662,875 4,988,626 2,494,313 7,482,940 3,741,470 1,870,735 5,612,206 2,806,103 8,418,310 4,209,155 12,627,466 6,313,733 18,941,200 9,470,600 4,735,300 2,367,650 1,183,825 3,551,476 1,775,738 887,869 2,663,608 1,331,804 665,902 332,951 998,854 499,427 1,498,282 749,141 2,247,424 1,123,712 561,856 280,928

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