205,500

2² × 3 × 5³ × 137

Starting at 205,500, the Collatz iteration reaches 1 after 98 steps. The first transition is 102750; the starting value is even with 48 positive divisors.

Prime Factor Structure

Factorization String 2^2 × 3 × 5^3 × 137

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 48

Divisor Sum (σ) 602,784

Proper Divisor Sum 397,284

Digit Sum / Digital Root 12 (Root: 3)

Adjacent Primes #205493 ← → #205507

Radix Representation

Decimal	205500
Binary	110010001010111100 (18 bits)
Octal	0o621274
Hexadecimal	0x322BC

Divisor Catalog (48)

1 2 3 4 5 6 10 12 15 20 25 30 50 60 75 100 125 137 150 250 274 300 375 411 500 548 685 750 822 1,370 1,500 1,644 2,055 2,740 3,425 4,110 6,850 8,220 10,275 13,700 17,125 20,550 34,250 41,100 51,375 68,500 102,750 205,500

Collatz Trajectory (98 steps to reach 1)

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

205,500 102,750 51,375 154,126 77,063 231,190 115,595 346,786 173,393 520,180 260,090 130,045 390,136 195,068 97,534 48,767 146,302 73,151 219,454 109,727 329,182 164,591 493,774 246,887 740,662 370,331 1,110,994 555,497 1,666,492 833,246 416,623 1,249,870 624,935 1,874,806 937,403 2,812,210 1,406,105 4,218,316 2,109,158 1,054,579 3,163,738 1,581,869 4,745,608 2,372,804 1,186,402 593,201 1,779,604 889,802 444,901 1,334,704 667,352 333,676 166,838 83,419 250,258 125,129 375,388 187,694 93,847 281,542

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