λ
Harmonic Matrix

173,744

24 × 10859
Deficient Even Composite

173,744 has digital root 8. The neighboring primes are 173743 and 173773; its proper-divisor sum differs from the starting integer by -10,828.

Prime Factor Structure

Factorization String 2^4 × 10859
Distinct Prime Factors 2
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 10
Divisor Sum (σ) 336,660
Proper Divisor Sum 162,916
Digit Sum / Digital Root 26 (Root: 8)
Adjacent Primes #173743 ← → #173773

Radix Representation

Decimal 173744
Binary 101010011010110000 (18 bits)
Octal 0o523260
Hexadecimal 0x2A6B0

Divisor Catalog (10)

1 2 4 8 16 10,859 21,718 43,436 86,872 173,744

Collatz Trajectory (46 steps to reach 1)

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

173,744 86,872 43,436 21,718 10,859 32,578 16,289 48,868 24,434 12,217 36,652 18,326 9,163 27,490 13,745 41,236 20,618 10,309 30,928 15,464 7,732 3,866 1,933 5,800 2,900 1,450 725 2,176 1,088 544 272 136 68 34 17 52 26 13 40 20 10 5 16 8 4 2 1

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