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Atlas › Integer Profiles › Node 72,084,006

72,084,006

2 × 35 × 83 × 1787
Abundant Even Composite

Prime Factor Structure

Factorization String 2 × 3^5 × 83 × 1787
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 164,009,664
Proper Divisor Sum 91,925,658
Digit Sum / Digital Root 27 (Root: 9)
Adjacent Primes #72083993 ← → #72084013

Radix Representation

Decimal 72084006
Binary 100010010111110101000100110 (27 bits)
Octal 0o422765046
Hexadecimal 0x44BEA26

Divisor Catalog (48)

1 2 3 6 9 18 27 54 81 83 162 166 243 249 486 498 747 1,494 1,787 2,241 3,574 4,482 5,361 6,723 10,722 13,446 16,083 20,169 32,166 40,338 48,249 96,498 144,747 148,321 289,494 296,642 434,241 444,963 868,482 889,926 1,334,889 2,669,778 4,004,667 8,009,334 12,014,001 24,028,002 36,042,003 72,084,006

Collatz Trajectory (140 steps to reach 1)

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

72,084,006 36,042,003 108,126,010 54,063,005 162,189,016 81,094,508 40,547,254 20,273,627 60,820,882 30,410,441 91,231,324 45,615,662 22,807,831 68,423,494 34,211,747 102,635,242 51,317,621 153,952,864 76,976,432 38,488,216 19,244,108 9,622,054 4,811,027 14,433,082 7,216,541 21,649,624 10,824,812 5,412,406 2,706,203 8,118,610 4,059,305 12,177,916 6,088,958 3,044,479 9,133,438 4,566,719 13,700,158 6,850,079 20,550,238 10,275,119 30,825,358 15,412,679 46,238,038 23,119,019 69,357,058 34,678,529 104,035,588 52,017,794 26,008,897 78,026,692 39,013,346 19,506,673 58,520,020 29,260,010 14,630,005 43,890,016 21,945,008 10,972,504 5,486,252 2,743,126

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