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Atlas › Integer Profiles › Node 12,972,192

12,972,192

25 × 3 × 163 × 829
Abundant Even Composite

12,972,192 factors as 2^5 × 3 × 163 × 829. Its 48 positive divisors give a proper-divisor sum of 21,330,048, so this integer is abundant. The Collatz stopping time is 197 steps.

Prime Factor Structure

Factorization String 2^5 × 3 × 163 × 829
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 34,302,240
Proper Divisor Sum 21,330,048
Digit Sum / Digital Root 33 (Root: 6)
Adjacent Primes #12972149 ← → #12972217

Radix Representation

Decimal 12972192
Binary 110001011111000010100000 (24 bits)
Octal 0o61370240
Hexadecimal 0xC5F0A0

Divisor Catalog (48)

1 2 3 4 6 8 12 16 24 32 48 96 163 326 489 652 829 978 1,304 1,658 1,956 2,487 2,608 3,316 3,912 4,974 5,216 6,632 7,824 9,948 13,264 15,648 19,896 26,528 39,792 79,584 135,127 270,254 405,381 540,508 810,762 1,081,016 1,621,524 2,162,032 3,243,048 4,324,064 6,486,096 12,972,192

Collatz Trajectory (197 steps to reach 1)

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

12,972,192 6,486,096 3,243,048 1,621,524 810,762 405,381 1,216,144 608,072 304,036 152,018 76,009 228,028 114,014 57,007 171,022 85,511 256,534 128,267 384,802 192,401 577,204 288,602 144,301 432,904 216,452 108,226 54,113 162,340 81,170 40,585 121,756 60,878 30,439 91,318 45,659 136,978 68,489 205,468 102,734 51,367 154,102 77,051 231,154 115,577 346,732 173,366 86,683 260,050 130,025 390,076 195,038 97,519 292,558 146,279 438,838 219,419 658,258 329,129 987,388 493,694

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