517,536

2⁵ × 3³ × 599

517,536 factors as 2^5 × 3^3 × 599. Its 48 positive divisors give a proper-divisor sum of 994,464, so this integer is abundant. The Collatz stopping time is 32 steps.

Prime Factor Structure

Factorization String 2^5 × 3^3 × 599

Distinct Prime Factors 3

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 48

Divisor Sum (σ) 1,512,000

Proper Divisor Sum 994,464

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #517513 ← → #517547

Radix Representation

Decimal	517536
Binary	1111110010110100000 (19 bits)
Octal	0o1762640
Hexadecimal	0x7E5A0

Divisor Catalog (48)

1 2 3 4 6 8 9 12 16 18 24 27 32 36 48 54 72 96 108 144 216 288 432 599 864 1,198 1,797 2,396 3,594 4,792 5,391 7,188 9,584 10,782 14,376 16,173 19,168 21,564 28,752 32,346 43,128 57,504 64,692 86,256 129,384 172,512 258,768 517,536

Collatz Trajectory (32 steps to reach 1)

Iterative sequence n → n/2 (if even) or 3n+1 (if odd):

517,536 258,768 129,384 64,692 32,346 16,173 48,520 24,260 12,130 6,065 18,196 9,098 4,549 13,648 6,824 3,412 1,706 853 2,560 1,280 640 320 160 80 40 20 10 5 16 8 4 2 1

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