λ
Harmonic Matrix

129,507

3 × 72 × 881
Deficient Odd Composite

129,507 has digital root 6. The neighboring primes are 129499 and 129509; its proper-divisor sum differs from the starting integer by -57,918.

Prime Factor Structure

Factorization String 3 × 7^2 × 881
Distinct Prime Factors 3
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 12
Divisor Sum (σ) 201,096
Proper Divisor Sum 71,589
Digit Sum / Digital Root 24 (Root: 6)
Adjacent Primes #129499 ← → #129509

Radix Representation

Decimal 129507
Binary 11111100111100011 (17 bits)
Octal 0o374743
Hexadecimal 0x1F9E3

Divisor Catalog (12)

1 3 7 21 49 147 881 2,643 6,167 18,501 43,169 129,507

Collatz Trajectory (162 steps to reach 1)

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

129,507 388,522 194,261 582,784 291,392 145,696 72,848 36,424 18,212 9,106 4,553 13,660 6,830 3,415 10,246 5,123 15,370 7,685 23,056 11,528 5,764 2,882 1,441 4,324 2,162 1,081 3,244 1,622 811 2,434 1,217 3,652 1,826 913 2,740 1,370 685 2,056 1,028 514 257 772 386 193 580 290 145 436 218 109 328 164 82 41 124 62 31 94 47 142

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