λ
Harmonic Matrix

409,296

24 × 3 × 8527
Abundant Even Composite

409,296 has digital root 3. The neighboring primes are 409291 and 409327; its proper-divisor sum differs from the starting integer by 238,880.

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Prime Factor Structure

Factorization String 2^4 × 3 × 8527
Distinct Prime Factors 3
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 20
Divisor Sum (σ) 1,057,472
Proper Divisor Sum 648,176
Digit Sum / Digital Root 30 (Root: 3)
Adjacent Primes #409291 ← → #409327

Radix Representation

Decimal 409296
Binary 1100011111011010000 (19 bits)
Octal 0o1437320
Hexadecimal 0x63ED0

Divisor Catalog (5 of 20)

1 2 3 4 6

Collatz Trajectory (130 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.

409,296 204,648 102,324 51,162 25,581

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