λ
Harmonic Matrix

8,013,657

3 × 29 × 92111
Deficient Odd Composite

8,013,657 has digital root 3. The neighboring primes are 8013623 and 8013659; its proper-divisor sum differs from the starting integer by -4,973,874.

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Prime Factor Structure

Factorization String 3 × 29 × 92111
Distinct Prime Factors 3
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 8
Divisor Sum (σ) 11,053,440
Proper Divisor Sum 3,039,783
Digit Sum / Digital Root 30 (Root: 3)
Adjacent Primes #8013623 ← → #8013659

Radix Representation

Decimal 8013657
Binary 11110100100011101011001 (23 bits)
Octal 0o36443531
Hexadecimal 0x7A4759

Divisor Catalog (5 of 8)

1 3 29 87 92,111

Collatz Trajectory (142 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.

8,013,657 24,040,972 12,020,486 6,010,243 18,030,730

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