λ
Harmonic Matrix

8,500,400

24 × 52 × 79 × 269
Abundant Even Composite

8,500,400 has digital root 8. The neighboring primes are 8500399 and 8500403; its proper-divisor sum differs from the starting integer by 3,756,800.

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Prime Factor Structure

Factorization String 2^4 × 5^2 × 79 × 269
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 60
Divisor Sum (σ) 20,757,600
Proper Divisor Sum 12,257,200
Digit Sum / Digital Root 17 (Root: 8)
Adjacent Primes #8500399 ← → #8500403

Radix Representation

Decimal 8500400
Binary 100000011011010010110000 (24 bits)
Octal 0o40332260
Hexadecimal 0x81B4B0

Divisor Catalog (5 of 60)

1 2 4 5 8

Collatz Trajectory (150 steps to reach 1)

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

Showing the first 5 trajectory entries; the stopping-time total above is unchanged.

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