λ
Harmonic Matrix

867,156

22 × 3 × 127 × 569
Abundant Even Composite

867,156 has digital root 6. The neighboring primes are 867151 and 867161; its proper-divisor sum differs from the starting integer by 308,568.

Prime Factor Structure

Factorization String 2^2 × 3 × 127 × 569
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 24
Divisor Sum (σ) 2,042,880
Proper Divisor Sum 1,175,724
Digit Sum / Digital Root 33 (Root: 6)
Adjacent Primes #867151 ← → #867161

Radix Representation

Decimal 867156
Binary 11010011101101010100 (20 bits)
Octal 0o3235524
Hexadecimal 0xD3B54

Divisor Catalog (24)

1 2 3 4 6 12 127 254 381 508 569 762 1,138 1,524 1,707 2,276 3,414 6,828 72,263 144,526 216,789 289,052 433,578 867,156

Collatz Trajectory (51 steps to reach 1)

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

867,156 433,578 216,789 650,368 325,184 162,592 81,296 40,648 20,324 10,162 5,081 15,244 7,622 3,811 11,434 5,717 17,152 8,576 4,288 2,144 1,072 536 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1

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