1,261,456

2⁴ × 7² × 1609

Starting at 1,261,456, the Collatz iteration reaches 1 after 80 steps. The first transition is 630728; the starting value is even with 30 positive divisors.

Prime Factor Structure

Factorization String 2^4 × 7^2 × 1609

Distinct Prime Factors 3

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 30

Divisor Sum (σ) 2,844,870

Proper Divisor Sum 1,583,414

Digit Sum / Digital Root 25 (Root: 7)

Adjacent Primes #1261427 ← → #1261459

Radix Representation

Decimal	1261456
Binary	100110011111110010000 (21 bits)
Octal	0o4637620
Hexadecimal	0x133F90

Divisor Catalog (30)

1 2 4 7 8 14 16 28 49 56 98 112 196 392 784 1,609 3,218 6,436 11,263 12,872 22,526 25,744 45,052 78,841 90,104 157,682 180,208 315,364 630,728 1,261,456

Collatz Trajectory (80 steps to reach 1)

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

1,261,456 630,728 315,364 157,682 78,841 236,524 118,262 59,131 177,394 88,697 266,092 133,046 66,523 199,570 99,785 299,356 149,678 74,839 224,518 112,259 336,778 168,389 505,168 252,584 126,292 63,146 31,573 94,720 47,360 23,680 11,840 5,920 2,960 1,480 740 370 185 556 278 139 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38

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