656,292

2² × 3 × 7 × 13 × 601

Starting at 656,292, the Collatz iteration reaches 1 after 154 steps. The first transition is 328146; the starting value is even with 48 positive divisors.

Prime Factor Structure

Factorization String 2^2 × 3 × 7 × 13 × 601

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 48

Divisor Sum (σ) 1,887,872

Proper Divisor Sum 1,231,580

Digit Sum / Digital Root 30 (Root: 3)

Adjacent Primes #656291 ← → #656297

Radix Representation

Decimal	656292
Binary	10100000001110100100 (20 bits)
Octal	0o2401644
Hexadecimal	0xA03A4

Divisor Catalog (48)

1 2 3 4 6 7 12 13 14 21 26 28 39 42 52 78 84 91 156 182 273 364 546 601 1,092 1,202 1,803 2,404 3,606 4,207 7,212 7,813 8,414 12,621 15,626 16,828 23,439 25,242 31,252 46,878 50,484 54,691 93,756 109,382 164,073 218,764 328,146 656,292

Collatz Trajectory (154 steps to reach 1)

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

656,292 328,146 164,073 492,220 246,110 123,055 369,166 184,583 553,750 276,875 830,626 415,313 1,245,940 622,970 311,485 934,456 467,228 233,614 116,807 350,422 175,211 525,634 262,817 788,452 394,226 197,113 591,340 295,670 147,835 443,506 221,753 665,260 332,630 166,315 498,946 249,473 748,420 374,210 187,105 561,316 280,658 140,329 420,988 210,494 105,247 315,742 157,871 473,614 236,807 710,422 355,211 1,065,634 532,817 1,598,452 799,226 399,613 1,198,840 599,420 299,710 149,855

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