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Atlas › Integer Profiles › Node 12,138,500

12,138,500

22 × 53 × 11 × 2207
Abundant Even Composite

12,138,500 factors as 2^2 × 5^3 × 11 × 2207. Its 48 positive divisors give a proper-divisor sum of 16,795,132, so this integer is abundant. The Collatz stopping time is 135 steps.

Prime Factor Structure

Factorization String 2^2 × 5^3 × 11 × 2207
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 28,933,632
Proper Divisor Sum 16,795,132
Digit Sum / Digital Root 20 (Root: 2)
Adjacent Primes #12138499 ← → #12138521

Radix Representation

Decimal 12138500
Binary 101110010011100000000100 (24 bits)
Octal 0o56234004
Hexadecimal 0xB93804

Divisor Catalog (48)

1 2 4 5 10 11 20 22 25 44 50 55 100 110 125 220 250 275 500 550 1,100 1,375 2,207 2,750 4,414 5,500 8,828 11,035 22,070 24,277 44,140 48,554 55,175 97,108 110,350 121,385 220,700 242,770 275,875 485,540 551,750 606,925 1,103,500 1,213,850 2,427,700 3,034,625 6,069,250 12,138,500

Collatz Trajectory (135 steps to reach 1)

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

12,138,500 6,069,250 3,034,625 9,103,876 4,551,938 2,275,969 6,827,908 3,413,954 1,706,977 5,120,932 2,560,466 1,280,233 3,840,700 1,920,350 960,175 2,880,526 1,440,263 4,320,790 2,160,395 6,481,186 3,240,593 9,721,780 4,860,890 2,430,445 7,291,336 3,645,668 1,822,834 911,417 2,734,252 1,367,126 683,563 2,050,690 1,025,345 3,076,036 1,538,018 769,009 2,307,028 1,153,514 576,757 1,730,272 865,136 432,568 216,284 108,142 54,071 162,214 81,107 243,322 121,661 364,984 182,492 91,246 45,623 136,870 68,435 205,306 102,653 307,960 153,980 76,990

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