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Math Directory

399,516

22 × 3 × 132 × 197
Abundant Even Composite

399,516 factors as 2^2 × 3 × 13^2 × 197. Its 36 positive divisors give a proper-divisor sum of 615,036, so this integer is abundant. The Collatz stopping time is 55 steps.

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Prime Factor Structure

Factorization String 2^2 × 3 × 13^2 × 197
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 36
Divisor Sum (σ) 1,014,552
Proper Divisor Sum 615,036
Digit Sum / Digital Root 33 (Root: 6)
Adjacent Primes #399499 ← → #399523

Radix Representation

Decimal 399516
Binary 1100001100010011100 (19 bits)
Octal 0o1414234
Hexadecimal 0x6189C

Divisor Catalog (5 of 36)

1 2 3 4 6

Collatz Trajectory (55 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.

399,516 199,758 99,879 299,638 149,819

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