λ
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Atlas › Integer Profiles › Node 72,025,209

72,025,209

32 × 17 × 223 × 2111
Deficient Odd Composite

72,025,209 factors as 3^2 × 17 × 223 × 2111. Its 24 positive divisors give a proper-divisor sum of 38,677,383, so this integer is deficient. The Collatz stopping time is 215 steps.

Prime Factor Structure

Factorization String 3^2 × 17 × 223 × 2111
Distinct Prime Factors 4
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 24
Divisor Sum (σ) 110,702,592
Proper Divisor Sum 38,677,383
Digit Sum / Digital Root 27 (Root: 9)
Adjacent Primes #72025207 ← → #72025211

Radix Representation

Decimal 72025209
Binary 100010010110000010001111001 (27 bits)
Octal 0o422602171
Hexadecimal 0x44B0479

Divisor Catalog (24)

1 3 9 17 51 153 223 669 2,007 2,111 3,791 6,333 11,373 18,999 34,119 35,887 107,661 322,983 470,753 1,412,259 4,236,777 8,002,801 24,008,403 72,025,209

Collatz Trajectory (215 steps to reach 1)

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

72,025,209 216,075,628 108,037,814 54,018,907 162,056,722 81,028,361 243,085,084 121,542,542 60,771,271 182,313,814 91,156,907 273,470,722 136,735,361 410,206,084 205,103,042 102,551,521 307,654,564 153,827,282 76,913,641 230,740,924 115,370,462 57,685,231 173,055,694 86,527,847 259,583,542 129,791,771 389,375,314 194,687,657 584,062,972 292,031,486 146,015,743 438,047,230 219,023,615 657,070,846 328,535,423 985,606,270 492,803,135 1,478,409,406 739,204,703 2,217,614,110 1,108,807,055 3,326,421,166 1,663,210,583 4,989,631,750 2,494,815,875 7,484,447,626 3,742,223,813 11,226,671,440 5,613,335,720 2,806,667,860 1,403,333,930 701,666,965 2,105,000,896 1,052,500,448 526,250,224 263,125,112 131,562,556 65,781,278 32,890,639 98,671,918

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