λ
Harmonic Matrix

76,049

113 × 673
Deficient Odd Composite

76,049 has digital root 8. The neighboring primes are 76039 and 76079; its proper-divisor sum differs from the starting integer by -75,262.

Prime Factor Structure

Factorization String 113 × 673
Distinct Prime Factors 2
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 4
Divisor Sum (σ) 76,836
Proper Divisor Sum 787
Digit Sum / Digital Root 26 (Root: 8)
Adjacent Primes #76039 ← → #76079

Radix Representation

Decimal 76049
Binary 10010100100010001 (17 bits)
Octal 0o224421
Hexadecimal 0x12911

Divisor Catalog (4)

1 113 673 76,049

Collatz Trajectory (125 steps to reach 1)

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

76,049 228,148 114,074 57,037 171,112 85,556 42,778 21,389 64,168 32,084 16,042 8,021 24,064 12,032 6,016 3,008 1,504 752 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1,186 593 1,780 890 445 1,336 668 334 167 502

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