9,802,205

5 × 7² × 40009

Starting at 9,802,205, the Collatz iteration reaches 1 after 88 steps. The first transition is 29406616; the starting value is odd with 12 positive divisors.

Prime Factor Structure

Factorization String 5 × 7^2 × 40009

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 12

Divisor Sum (σ) 13,683,420

Proper Divisor Sum 3,881,215

Digit Sum / Digital Root 26 (Root: 8)

Adjacent Primes #9802181 ← → #9802211

Radix Representation

Decimal	9802205
Binary	100101011001000111011101 (24 bits)
Octal	0o45310735
Hexadecimal	0x9591DD

Divisor Catalog (12)

1 5 7 35 49 245 40,009 200,045 280,063 1,400,315 1,960,441 9,802,205

Collatz Trajectory (88 steps to reach 1)

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

9,802,205 29,406,616 14,703,308 7,351,654 3,675,827 11,027,482 5,513,741 16,541,224 8,270,612 4,135,306 2,067,653 6,202,960 3,101,480 1,550,740 775,370 387,685 1,163,056 581,528 290,764 145,382 72,691 218,074 109,037 327,112 163,556 81,778 40,889 122,668 61,334 30,667 92,002 46,001 138,004 69,002 34,501 103,504 51,752 25,876 12,938 6,469 19,408 9,704 4,852 2,426 1,213 3,640 1,820 910 455 1,366 683 2,050 1,025 3,076 1,538 769 2,308 1,154 577 1,732

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