λ
Harmonic Matrix

8,357,265

32 × 5 × 7 × 43 × 617
Abundant Odd Composite

8,357,265 has digital root 9. The neighboring primes are 8357233 and 8357269; its proper-divisor sum differs from the starting integer by 253,278.

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Prime Factor Structure

Factorization String 3^2 × 5 × 7 × 43 × 617
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 16,967,808
Proper Divisor Sum 8,610,543
Digit Sum / Digital Root 36 (Root: 9)
Adjacent Primes #8357233 ← → #8357269

Radix Representation

Decimal 8357265
Binary 11111111000010110010001 (23 bits)
Octal 0o37702621
Hexadecimal 0x7F8591

Divisor Catalog (5 of 48)

1 3 5 7 9

Collatz Trajectory (137 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.

8,357,265 25,071,796 12,535,898 6,267,949 18,803,848

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