8,197,137

3² × 13 × 70061

8,197,137 factors as 3^2 × 13 × 70061. Its 12 positive divisors give a proper-divisor sum of 4,554,147, so this integer is deficient. The Collatz stopping time is 199 steps.

Prime Factor Structure

Factorization String 3^2 × 13 × 70061

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 12

Divisor Sum (σ) 12,751,284

Proper Divisor Sum 4,554,147

Digit Sum / Digital Root 36 (Root: 9)

Adjacent Primes #8197099 ← → #8197141

Radix Representation

Decimal	8197137
Binary	11111010001010000010001 (23 bits)
Octal	0o37212021
Hexadecimal	0x7D1411

Divisor Catalog (12)

1 3 9 13 39 117 70,061 210,183 630,549 910,793 2,732,379 8,197,137

Collatz Trajectory (199 steps to reach 1)

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

8,197,137 24,591,412 12,295,706 6,147,853 18,443,560 9,221,780 4,610,890 2,305,445 6,916,336 3,458,168 1,729,084 864,542 432,271 1,296,814 648,407 1,945,222 972,611 2,917,834 1,458,917 4,376,752 2,188,376 1,094,188 547,094 273,547 820,642 410,321 1,230,964 615,482 307,741 923,224 461,612 230,806 115,403 346,210 173,105 519,316 259,658 129,829 389,488 194,744 97,372 48,686 24,343 73,030 36,515 109,546 54,773 164,320 82,160 41,080 20,540 10,270 5,135 15,406 7,703 23,110 11,555 34,666 17,333 52,000

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