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Atlas › Integer Profiles › Node 72,394,896

72,394,896

24 × 3 × 7 × 215461
Abundant Even Composite

72,394,896 factors as 2^4 × 3 × 7 × 215461. Its 40 positive divisors give a proper-divisor sum of 141,343,408, so this integer is abundant. The Collatz stopping time is 140 steps.

Prime Factor Structure

Factorization String 2^4 × 3 × 7 × 215461
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 40
Divisor Sum (σ) 213,738,304
Proper Divisor Sum 141,343,408
Digit Sum / Digital Root 48 (Root: 3)
Adjacent Primes #72394877 ← → #72394897

Radix Representation

Decimal 72394896
Binary 100010100001010100010010000 (27 bits)
Octal 0o424124220
Hexadecimal 0x450A890

Divisor Catalog (40)

1 2 3 4 6 7 8 12 14 16 21 24 28 42 48 56 84 112 168 336 215,461 430,922 646,383 861,844 1,292,766 1,508,227 1,723,688 2,585,532 3,016,454 3,447,376 4,524,681 5,171,064 6,032,908 9,049,362 10,342,128 12,065,816 18,098,724 24,131,632 36,197,448 72,394,896

Collatz Trajectory (140 steps to reach 1)

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

72,394,896 36,197,448 18,098,724 9,049,362 4,524,681 13,574,044 6,787,022 3,393,511 10,180,534 5,090,267 15,270,802 7,635,401 22,906,204 11,453,102 5,726,551 17,179,654 8,589,827 25,769,482 12,884,741 38,654,224 19,327,112 9,663,556 4,831,778 2,415,889 7,247,668 3,623,834 1,811,917 5,435,752 2,717,876 1,358,938 679,469 2,038,408 1,019,204 509,602 254,801 764,404 382,202 191,101 573,304 286,652 143,326 71,663 214,990 107,495 322,486 161,243 483,730 241,865 725,596 362,798 181,399 544,198 272,099 816,298 408,149 1,224,448 612,224 306,112 153,056 76,528

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