λ
Harmonic Matrix

506,688

26 × 3 × 7 × 13 × 29
Abundant Even Composite

506,688 has digital root 6. The neighboring primes are 506687 and 506689; its proper-divisor sum differs from the starting integer by 693,504.

Prime Factor Structure

Factorization String 2^6 × 3 × 7 × 13 × 29
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 112
Divisor Sum (σ) 1,706,880
Proper Divisor Sum 1,200,192
Digit Sum / Digital Root 33 (Root: 6)
Adjacent Primes #506687 ← → #506689

Radix Representation

Decimal 506688
Binary 1111011101101000000 (19 bits)
Octal 0o1735500
Hexadecimal 0x7BB40

Divisor Catalog (60 of 112)

Collatz Trajectory (151 steps to reach 1)

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

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