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Atlas › Integer Profiles › Node 8,520,192

8,520,192

29 × 32 × 432
Abundant Even Composite

8,520,192 factors as 2^9 × 3^2 × 43^2. Its 90 positive divisors give a proper-divisor sum of 16,654,815, so this integer is abundant. The Collatz stopping time is 62 steps.

Prime Factor Structure

Factorization String 2^9 × 3^2 × 43^2
Distinct Prime Factors 3
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 90
Divisor Sum (σ) 25,175,007
Proper Divisor Sum 16,654,815
Digit Sum / Digital Root 27 (Root: 9)
Adjacent Primes #8520191 ← → #8520241

Radix Representation

Decimal 8520192
Binary 100000100000001000000000 (24 bits)
Octal 0o40401000
Hexadecimal 0x820200

Divisor Catalog (60 of 90)

1 2 3 4 6 8 9 12 16 18 24 32 36 43 48 64 72 86 96 128 129 144 172 192 256 258 288 344 384 387 512 516 576 688 768 774 1,032 1,152 1,376 1,536 1,548 1,849 2,064 2,304 2,752 3,096 3,698 4,128 4,608 5,504 5,547 6,192 7,396 8,256 11,008 11,094 12,384 14,792 16,512 16,641

Collatz Trajectory (62 steps to reach 1)

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

8,520,192 4,260,096 2,130,048 1,065,024 532,512 266,256 133,128 66,564 33,282 16,641 49,924 24,962 12,481 37,444 18,722 9,361 28,084 14,042 7,021 21,064 10,532 5,266 2,633 7,900 3,950 1,975 5,926 2,963 8,890 4,445 13,336 6,668 3,334 1,667 5,002 2,501 7,504 3,752 1,876 938 469 1,408 704 352 176 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8

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