λ
Harmonic Matrix

5,109,840

24 × 32 × 5 × 47 × 151
Abundant Even Composite

5,109,840 has digital root 9. The neighboring primes are 5109821 and 5109847; its proper-divisor sum differs from the starting integer by 7,422,048.

Prime Factor Structure

Factorization String 2^4 × 3^2 × 5 × 47 × 151
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 120
Divisor Sum (σ) 17,641,728
Proper Divisor Sum 12,531,888
Digit Sum / Digital Root 27 (Root: 9)
Adjacent Primes #5109821 ← → #5109847

Radix Representation

Decimal 5109840
Binary 10011011111100001010000 (23 bits)
Octal 0o23374120
Hexadecimal 0x4DF850

Divisor Catalog (60 of 120)

1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 30 36 40 45 47 48 60 72 80 90 94 120 141 144 151 180 188 235 240 282 302 360 376 423 453 470 564 604 705 720 752 755 846 906 940 1,128 1,208 1,359 1,410 1,510 1,692 1,812 1,880 2,115 2,256

Collatz Trajectory (113 steps to reach 1)

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

5,109,840 2,554,920 1,277,460 638,730 319,365 958,096 479,048 239,524 119,762 59,881 179,644 89,822 44,911 134,734 67,367 202,102 101,051 303,154 151,577 454,732 227,366 113,683 341,050 170,525 511,576 255,788 127,894 63,947 191,842 95,921 287,764 143,882 71,941 215,824 107,912 53,956 26,978 13,489 40,468 20,234 10,117 30,352 15,176 7,588 3,794 1,897 5,692 2,846 1,423 4,270 2,135 6,406 3,203 9,610 4,805 14,416 7,208 3,604 1,802 901

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