198,441

3² × 17 × 1297

198,441 factors as 3^2 × 17 × 1297. Its 12 positive divisors give a proper-divisor sum of 105,291, so this integer is deficient. The Collatz stopping time is 147 steps.

Prime Factor Structure

Factorization String 3^2 × 17 × 1297

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 12

Divisor Sum (σ) 303,732

Proper Divisor Sum 105,291

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #198439 ← → #198461

Radix Representation

Decimal	198441
Binary	110000011100101001 (18 bits)
Octal	0o603451
Hexadecimal	0x30729

Divisor Catalog (12)

1 3 9 17 51 153 1,297 3,891 11,673 22,049 66,147 198,441

Collatz Trajectory (147 steps to reach 1)

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

198,441 595,324 297,662 148,831 446,494 223,247 669,742 334,871 1,004,614 502,307 1,506,922 753,461 2,260,384 1,130,192 565,096 282,548 141,274 70,637 211,912 105,956 52,978 26,489 79,468 39,734 19,867 59,602 29,801 89,404 44,702 22,351 67,054 33,527 100,582 50,291 150,874 75,437 226,312 113,156 56,578 28,289 84,868 42,434 21,217 63,652 31,826 15,913 47,740 23,870 11,935 35,806 17,903 53,710 26,855 80,566 40,283 120,850 60,425 181,276 90,638 45,319

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