λ
Harmonic Matrix

8,409,688

23 × 7 × 263 × 571
Abundant Even Composite

8,409,688 has digital root 7. The neighboring primes are 8409671 and 8409689; its proper-divisor sum differs from the starting integer by 1,301,584.

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Prime Factor Structure

Factorization String 2^3 × 7 × 263 × 571
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 32
Divisor Sum (σ) 18,120,960
Proper Divisor Sum 9,711,272
Digit Sum / Digital Root 43 (Root: 7)
Adjacent Primes #8409671 ← → #8409689

Radix Representation

Decimal 8409688
Binary 100000000101001001011000 (24 bits)
Octal 0o40051130
Hexadecimal 0x805258

Divisor Catalog (5 of 32)

1 2 4 7 8

Collatz Trajectory (106 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.

8,409,688 4,204,844 2,102,422 1,051,211 3,153,634

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