λ
Harmonic Matrix

6,107,301

32 × 17 × 179 × 223
Deficient Odd Composite

6,107,301 has digital root 9. The neighboring primes are 6107293 and 6107317; its proper-divisor sum differs from the starting integer by -2,779,722.

Prime Factor Structure

Factorization String 3^2 × 17 × 179 × 223
Distinct Prime Factors 4
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 24
Divisor Sum (σ) 9,434,880
Proper Divisor Sum 3,327,579
Digit Sum / Digital Root 18 (Root: 9)
Adjacent Primes #6107293 ← → #6107317

Radix Representation

Decimal 6107301
Binary 10111010011000010100101 (23 bits)
Octal 0o27230245
Hexadecimal 0x5D30A5

Divisor Catalog (24)

1 3 9 17 51 153 179 223 537 669 1,611 2,007 3,043 3,791 9,129 11,373 27,387 34,119 39,917 119,751 359,253 678,589 2,035,767 6,107,301

Collatz Trajectory (134 steps to reach 1)

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

6,107,301 18,321,904 9,160,952 4,580,476 2,290,238 1,145,119 3,435,358 1,717,679 5,153,038 2,576,519 7,729,558 3,864,779 11,594,338 5,797,169 17,391,508 8,695,754 4,347,877 13,043,632 6,521,816 3,260,908 1,630,454 815,227 2,445,682 1,222,841 3,668,524 1,834,262 917,131 2,751,394 1,375,697 4,127,092 2,063,546 1,031,773 3,095,320 1,547,660 773,830 386,915 1,160,746 580,373 1,741,120 870,560 435,280 217,640 108,820 54,410 27,205 81,616 40,808 20,404 10,202 5,101 15,304 7,652 3,826 1,913 5,740 2,870 1,435 4,306 2,153 6,460

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