λ
Harmonic Matrix

8,822,832

24 × 3 × 183809
Abundant Even Composite

8,822,832 has digital root 6. The neighboring primes are 8822797 and 8822833; its proper-divisor sum differs from the starting integer by 5,146,776.

Prime Factor Structure

Factorization String 2^4 × 3 × 183809
Distinct Prime Factors 3
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 20
Divisor Sum (σ) 22,792,440
Proper Divisor Sum 13,969,608
Digit Sum / Digital Root 33 (Root: 6)
Adjacent Primes #8822797 ← → #8822833

Radix Representation

Decimal 8822832
Binary 100001101010000000110000 (24 bits)
Octal 0o41520060
Hexadecimal 0x86A030

Divisor Catalog (20)

1 2 3 4 6 8 12 16 24 48 183,809 367,618 551,427 735,236 1,102,854 1,470,472 2,205,708 2,940,944 4,411,416 8,822,832

Collatz Trajectory (88 steps to reach 1)

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

8,822,832 4,411,416 2,205,708 1,102,854 551,427 1,654,282 827,141 2,481,424 1,240,712 620,356 310,178 155,089 465,268 232,634 116,317 348,952 174,476 87,238 43,619 130,858 65,429 196,288 98,144 49,072 24,536 12,268 6,134 3,067 9,202 4,601 13,804 6,902 3,451 10,354 5,177 15,532 7,766 3,883 11,650 5,825 17,476 8,738 4,369 13,108 6,554 3,277 9,832 4,916 2,458 1,229 3,688 1,844 922 461 1,384 692 346 173 520 260

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