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Atlas › Integer Profiles › Node 72,012

72,012

22 × 3 × 17 × 353
Abundant Even Composite

Prime Factor Structure

Factorization String 2^2 × 3 × 17 × 353
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 24
Divisor Sum (σ) 178,416
Proper Divisor Sum 106,404
Digit Sum / Digital Root 12 (Root: 3)
Adjacent Primes #71999 ← → #72019

Radix Representation

Decimal 72012
Binary 10001100101001100 (17 bits)
Octal 0o214514
Hexadecimal 0x1194C

Divisor Catalog (24)

1 2 3 4 6 12 17 34 51 68 102 204 353 706 1,059 1,412 2,118 4,236 6,001 12,002 18,003 24,004 36,006 72,012

Collatz Trajectory (143 steps to reach 1)

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

72,012 36,006 18,003 54,010 27,005 81,016 40,508 20,254 10,127 30,382 15,191 45,574 22,787 68,362 34,181 102,544 51,272 25,636 12,818 6,409 19,228 9,614 4,807 14,422 7,211 21,634 10,817 32,452 16,226 8,113 24,340 12,170 6,085 18,256 9,128 4,564 2,282 1,141 3,424 1,712 856 428 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466

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