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Atlas › Integer Profiles › Node 72,040,100

72,040,100

22 × 52 × 11 × 79 × 829
Abundant Even Composite

Prime Factor Structure

Factorization String 2^2 × 5^2 × 11 × 79 × 829
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 72
Divisor Sum (σ) 172,905,600
Proper Divisor Sum 100,865,500
Digit Sum / Digital Root 14 (Root: 5)
Adjacent Primes #72040069 ← → #72040103

Radix Representation

Decimal 72040100
Binary 100010010110011111010100100 (27 bits)
Octal 0o422637244
Hexadecimal 0x44B3EA4

Divisor Catalog (60 of 72)

1 2 4 5 10 11 20 22 25 44 50 55 79 100 110 158 220 275 316 395 550 790 829 869 1,100 1,580 1,658 1,738 1,975 3,316 3,476 3,950 4,145 4,345 7,900 8,290 8,690 9,119 16,580 17,380 18,238 20,725 21,725 36,476 41,450 43,450 45,595 65,491 82,900 86,900 91,190 130,982 182,380 227,975 261,964 327,455 455,950 654,910 720,401 911,900

Collatz Trajectory (321 steps to reach 1)

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

72,040,100 36,020,050 18,010,025 54,030,076 27,015,038 13,507,519 40,522,558 20,261,279 60,783,838 30,391,919 91,175,758 45,587,879 136,763,638 68,381,819 205,145,458 102,572,729 307,718,188 153,859,094 76,929,547 230,788,642 115,394,321 346,182,964 173,091,482 86,545,741 259,637,224 129,818,612 64,909,306 32,454,653 97,363,960 48,681,980 24,340,990 12,170,495 36,511,486 18,255,743 54,767,230 27,383,615 82,150,846 41,075,423 123,226,270 61,613,135 184,839,406 92,419,703 277,259,110 138,629,555 415,888,666 207,944,333 623,833,000 311,916,500 155,958,250 77,979,125 233,937,376 116,968,688 58,484,344 29,242,172 14,621,086 7,310,543 21,931,630 10,965,815 32,897,446 16,448,723

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