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Atlas › Integer Profiles › Node 72,532,920

72,532,920

23 × 3 × 5 × 604441
Abundant Even Composite

72,532,920 factors as 2^3 × 3 × 5 × 604441. Its 32 positive divisors give a proper-divisor sum of 145,066,200, so this integer is abundant. The Collatz stopping time is 153 steps.

Prime Factor Structure

Factorization String 2^3 × 3 × 5 × 604441
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 32
Divisor Sum (σ) 217,599,120
Proper Divisor Sum 145,066,200
Digit Sum / Digital Root 30 (Root: 3)
Adjacent Primes #72532919 ← → #72532921

Radix Representation

Decimal 72532920
Binary 100010100101100001110111000 (27 bits)
Octal 0o424541670
Hexadecimal 0x452C3B8

Divisor Catalog (32)

1 2 3 4 5 6 8 10 12 15 20 24 30 40 60 120 604,441 1,208,882 1,813,323 2,417,764 3,022,205 3,626,646 4,835,528 6,044,410 7,253,292 9,066,615 12,088,820 14,506,584 18,133,230 24,177,640 36,266,460 72,532,920

Collatz Trajectory (153 steps to reach 1)

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

72,532,920 36,266,460 18,133,230 9,066,615 27,199,846 13,599,923 40,799,770 20,399,885 61,199,656 30,599,828 15,299,914 7,649,957 22,949,872 11,474,936 5,737,468 2,868,734 1,434,367 4,303,102 2,151,551 6,454,654 3,227,327 9,681,982 4,840,991 14,522,974 7,261,487 21,784,462 10,892,231 32,676,694 16,338,347 49,015,042 24,507,521 73,522,564 36,761,282 18,380,641 55,141,924 27,570,962 13,785,481 41,356,444 20,678,222 10,339,111 31,017,334 15,508,667 46,526,002 23,263,001 69,789,004 34,894,502 17,447,251 52,341,754 26,170,877 78,512,632 39,256,316 19,628,158 9,814,079 29,442,238 14,721,119 44,163,358 22,081,679 66,245,038 33,122,519 99,367,558

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