526,253

7 × 13 × 5783

Starting at 526,253, the Collatz iteration reaches 1 after 125 steps. The first transition is 1578760; the starting value is odd with 8 positive divisors.

Prime Factor Structure

Factorization String 7 × 13 × 5783

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 8

Divisor Sum (σ) 647,808

Proper Divisor Sum 121,555

Digit Sum / Digital Root 23 (Root: 5)

Adjacent Primes #526249 ← → #526271

Radix Representation

Decimal	526253
Binary	10000000011110101101 (20 bits)
Octal	0o2003655
Hexadecimal	0x807AD

Divisor Catalog (8)

1 7 13 91 5,783 40,481 75,179 526,253

Collatz Trajectory (125 steps to reach 1)

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

526,253 1,578,760 789,380 394,690 197,345 592,036 296,018 148,009 444,028 222,014 111,007 333,022 166,511 499,534 249,767 749,302 374,651 1,123,954 561,977 1,685,932 842,966 421,483 1,264,450 632,225 1,896,676 948,338 474,169 1,422,508 711,254 355,627 1,066,882 533,441 1,600,324 800,162 400,081 1,200,244 600,122 300,061 900,184 450,092 225,046 112,523 337,570 168,785 506,356 253,178 126,589 379,768 189,884 94,942 47,471 142,414 71,207 213,622 106,811 320,434 160,217 480,652 240,326 120,163

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