λ
Harmonic Matrix

164,469

3 × 73 × 751
Deficient Odd Composite

164,469 has digital root 3. The neighboring primes are 164449 and 164471; its proper-divisor sum differs from the starting integer by -106,346.

Prime Factor Structure

Factorization String 3 × 73 × 751
Distinct Prime Factors 3
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 8
Divisor Sum (σ) 222,592
Proper Divisor Sum 58,123
Digit Sum / Digital Root 30 (Root: 3)
Adjacent Primes #164449 ← → #164471

Radix Representation

Decimal 164469
Binary 101000001001110101 (18 bits)
Octal 0o501165
Hexadecimal 0x28275

Divisor Catalog (8)

1 3 73 219 751 2,253 54,823 164,469

Collatz Trajectory (152 steps to reach 1)

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

164,469 493,408 246,704 123,352 61,676 30,838 15,419 46,258 23,129 69,388 34,694 17,347 52,042 26,021 78,064 39,032 19,516 9,758 4,879 14,638 7,319 21,958 10,979 32,938 16,469 49,408 24,704 12,352 6,176 3,088 1,544 772 386 193 580 290 145 436 218 109 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182

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