829,216

2⁵ × 25913

829,216 has digital root 1. The neighboring primes are 829211 and 829223; its proper-divisor sum differs from the starting integer by -25,850.

Prime Factor Structure

Factorization String 2^5 × 25913

Distinct Prime Factors 2

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 12

Divisor Sum (σ) 1,632,582

Proper Divisor Sum 803,366

Digit Sum / Digital Root 28 (Root: 1)

Adjacent Primes #829211 ← → #829223

Radix Representation

Decimal	829216
Binary	11001010011100100000 (20 bits)
Octal	0o3123440
Hexadecimal	0xCA720

Divisor Catalog (12)

1 2 4 8 16 32 25,913 51,826 103,652 207,304 414,608 829,216

Collatz Trajectory (131 steps to reach 1)

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

829,216 414,608 207,304 103,652 51,826 25,913 77,740 38,870 19,435 58,306 29,153 87,460 43,730 21,865 65,596 32,798 16,399 49,198 24,599 73,798 36,899 110,698 55,349 166,048 83,024 41,512 20,756 10,378 5,189 15,568 7,784 3,892 1,946 973 2,920 1,460 730 365 1,096 548 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1,186 593 1,780 890

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