λ
Harmonic Matrix

7,197,648

24 × 3 × 113 × 1327
Abundant Even Composite

7,197,648 has digital root 6. The neighboring primes are 7197607 and 7197653; its proper-divisor sum differs from the starting integer by 4,377,312.

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Prime Factor Structure

Factorization String 2^4 × 3 × 113 × 1327
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 40
Divisor Sum (σ) 18,772,608
Proper Divisor Sum 11,574,960
Digit Sum / Digital Root 42 (Root: 6)
Adjacent Primes #7197607 ← → #7197653

Radix Representation

Decimal 7197648
Binary 11011011101001111010000 (23 bits)
Octal 0o33351720
Hexadecimal 0x6DD3D0

Divisor Catalog (5 of 40)

1 2 3 4 6

Collatz Trajectory (90 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.

7,197,648 3,598,824 1,799,412 899,706 449,853

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