838,101

3 × 11 × 109 × 233

Starting at 838,101, the Collatz iteration reaches 1 after 82 steps. The first transition is 2514304; the starting value is odd with 16 positive divisors.

Prime Factor Structure

Factorization String 3 × 11 × 109 × 233

Distinct Prime Factors 4

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 16

Divisor Sum (σ) 1,235,520

Proper Divisor Sum 397,419

Digit Sum / Digital Root 21 (Root: 3)

Adjacent Primes #838099 ← → #838133

Radix Representation

Decimal	838101
Binary	11001100100111010101 (20 bits)
Octal	0o3144725
Hexadecimal	0xCC9D5

Divisor Catalog (16)

1 3 11 33 109 233 327 699 1,199 2,563 3,597 7,689 25,397 76,191 279,367 838,101

Collatz Trajectory (82 steps to reach 1)

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

838,101 2,514,304 1,257,152 628,576 314,288 157,144 78,572 39,286 19,643 58,930 29,465 88,396 44,198 22,099 66,298 33,149 99,448 49,724 24,862 12,431 37,294 18,647 55,942 27,971 83,914 41,957 125,872 62,936 31,468 15,734 7,867 23,602 11,801 35,404 17,702 8,851 26,554 13,277 39,832 19,916 9,958 4,979 14,938 7,469 22,408 11,204 5,602 2,801 8,404 4,202 2,101 6,304 3,152 1,576 788 394 197 592 296 148

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