λ
Harmonic Matrix

130,039

7 × 13 × 1429
Deficient Odd Composite

130,039 has digital root 7. The neighboring primes are 130027 and 130043; its proper-divisor sum differs from the starting integer by -99,918.

Prime Factor Structure

Factorization String 7 × 13 × 1429
Distinct Prime Factors 3
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 8
Divisor Sum (σ) 160,160
Proper Divisor Sum 30,121
Digit Sum / Digital Root 16 (Root: 7)
Adjacent Primes #130027 ← → #130043

Radix Representation

Decimal 130039
Binary 11111101111110111 (17 bits)
Octal 0o375767
Hexadecimal 0x1FBF7

Divisor Catalog (8)

1 7 13 91 1,429 10,003 18,577 130,039

Collatz Trajectory (193 steps to reach 1)

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

130,039 390,118 195,059 585,178 292,589 877,768 438,884 219,442 109,721 329,164 164,582 82,291 246,874 123,437 370,312 185,156 92,578 46,289 138,868 69,434 34,717 104,152 52,076 26,038 13,019 39,058 19,529 58,588 29,294 14,647 43,942 21,971 65,914 32,957 98,872 49,436 24,718 12,359 37,078 18,539 55,618 27,809 83,428 41,714 20,857 62,572 31,286 15,643 46,930 23,465 70,396 35,198 17,599 52,798 26,399 79,198 39,599 118,798 59,399 178,198

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