λ
Harmonic Matrix

7,332,312

23 × 3 × 13 × 71 × 331
Abundant Even Composite

7,332,312 has digital root 3. The neighboring primes are 7332301 and 7332313; its proper-divisor sum differs from the starting integer by 5,414,736.

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Prime Factor Structure

Factorization String 2^3 × 3 × 13 × 71 × 331
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 64
Divisor Sum (σ) 20,079,360
Proper Divisor Sum 12,747,048
Digit Sum / Digital Root 21 (Root: 3)
Adjacent Primes #7332301 ← → #7332313

Radix Representation

Decimal 7332312
Binary 11011111110000111011000 (23 bits)
Octal 0o33760730
Hexadecimal 0x6FE1D8

Divisor Catalog (5 of 64)

1 2 3 4 6

Collatz Trajectory (160 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.

7,332,312 3,666,156 1,833,078 916,539 2,749,618

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