7,622,205

3 × 5 × 17 × 71 × 421

Starting at 7,622,205, the Collatz iteration reaches 1 after 111 steps. The first transition is 22866616; the starting value is odd with 32 positive divisors.

Prime Factor Structure

Factorization String 3 × 5 × 17 × 71 × 421

Distinct Prime Factors 5

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 32

Divisor Sum (σ) 13,125,888

Proper Divisor Sum 5,503,683

Digit Sum / Digital Root 24 (Root: 6)

Adjacent Primes #7622203 ← → #7622213

Radix Representation

Decimal	7622205
Binary	11101000100111000111101 (23 bits)
Octal	0o35047075
Hexadecimal	0x744E3D

Divisor Catalog (32)

1 3 5 15 17 51 71 85 213 255 355 421 1,065 1,207 1,263 2,105 3,621 6,035 6,315 7,157 18,105 21,471 29,891 35,785 89,673 107,355 149,455 448,365 508,147 1,524,441 2,540,735 7,622,205

Collatz Trajectory (111 steps to reach 1)

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

7,622,205 22,866,616 11,433,308 5,716,654 2,858,327 8,574,982 4,287,491 12,862,474 6,431,237 19,293,712 9,646,856 4,823,428 2,411,714 1,205,857 3,617,572 1,808,786 904,393 2,713,180 1,356,590 678,295 2,034,886 1,017,443 3,052,330 1,526,165 4,578,496 2,289,248 1,144,624 572,312 286,156 143,078 71,539 214,618 107,309 321,928 160,964 80,482 40,241 120,724 60,362 30,181 90,544 45,272 22,636 11,318 5,659 16,978 8,489 25,468 12,734 6,367 19,102 9,551 28,654 14,327 42,982 21,491 64,474 32,237 96,712 48,356

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