λ
Harmonic Matrix

7,713,000

23 × 32 × 53 × 857
Abundant Even Composite

7,713,000 has digital root 9. The neighboring primes are 7712989 and 7713047; its proper-divisor sum differs from the starting integer by 10,674,360.

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Prime Factor Structure

Factorization String 2^3 × 3^2 × 5^3 × 857
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 96
Divisor Sum (σ) 26,100,360
Proper Divisor Sum 18,387,360
Digit Sum / Digital Root 18 (Root: 9)
Adjacent Primes #7712989 ← → #7713047

Radix Representation

Decimal 7713000
Binary 11101011011000011101000 (23 bits)
Octal 0o35330350
Hexadecimal 0x75B0E8

Divisor Catalog (5 of 96)

1 2 3 4 5

Collatz Trajectory (72 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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