λ
Harmonic Matrix

106,125

3 × 53 × 283
Deficient Odd Composite

106,125 has digital root 6. The neighboring primes are 106123 and 106129; its proper-divisor sum differs from the starting integer by -35,034.

Prime Factor Structure

Factorization String 3 × 5^3 × 283
Distinct Prime Factors 3
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 16
Divisor Sum (σ) 177,216
Proper Divisor Sum 71,091
Digit Sum / Digital Root 15 (Root: 6)
Adjacent Primes #106123 ← → #106129

Radix Representation

Decimal 106125
Binary 11001111010001101 (17 bits)
Octal 0o317215
Hexadecimal 0x19E8D

Divisor Catalog (16)

1 3 5 15 25 75 125 283 375 849 1,415 4,245 7,075 21,225 35,375 106,125

Collatz Trajectory (79 steps to reach 1)

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

106,125 318,376 159,188 79,594 39,797 119,392 59,696 29,848 14,924 7,462 3,731 11,194 5,597 16,792 8,396 4,198 2,099 6,298 3,149 9,448 4,724 2,362 1,181 3,544 1,772 886 443 1,330 665 1,996 998 499 1,498 749 2,248 1,124 562 281 844 422 211 634 317 952 476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19

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