λ
Harmonic Matrix

509,649

3 × 72 × 3467
Deficient Odd Composite

509,649 has digital root 6. The neighboring primes are 509647 and 509653; its proper-divisor sum differs from the starting integer by -228,594.

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Prime Factor Structure

Factorization String 3 × 7^2 × 3467
Distinct Prime Factors 3
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 12
Divisor Sum (σ) 790,704
Proper Divisor Sum 281,055
Digit Sum / Digital Root 33 (Root: 6)
Adjacent Primes #509647 ← → #509653

Radix Representation

Decimal 509649
Binary 1111100011011010001 (19 bits)
Octal 0o1743321
Hexadecimal 0x7C6D1

Divisor Catalog (5 of 12)

1 3 7 21 49

Collatz Trajectory (81 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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