λ
Harmonic Matrix

8,237,192

23 × 991 × 1039
Deficient Even Composite

8,237,192 has digital root 5. The neighboring primes are 8237191 and 8237213; its proper-divisor sum differs from the starting integer by -999,184.

Prime Factor Structure

Factorization String 2^3 × 991 × 1039
Distinct Prime Factors 3
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 16
Divisor Sum (σ) 15,475,200
Proper Divisor Sum 7,238,008
Digit Sum / Digital Root 32 (Root: 5)
Adjacent Primes #8237191 ← → #8237213

Radix Representation

Decimal 8237192
Binary 11111011011000010001000 (23 bits)
Octal 0o37330210
Hexadecimal 0x7DB088

Divisor Catalog (16)

1 2 4 8 991 1,039 1,982 2,078 3,964 4,156 7,928 8,312 1,029,649 2,059,298 4,118,596 8,237,192

Collatz Trajectory (62 steps to reach 1)

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

8,237,192 4,118,596 2,059,298 1,029,649 3,088,948 1,544,474 772,237 2,316,712 1,158,356 579,178 289,589 868,768 434,384 217,192 108,596 54,298 27,149 81,448 40,724 20,362 10,181 30,544 15,272 7,636 3,818 1,909 5,728 2,864 1,432 716 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8

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