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Atlas › Integer Profiles › Node 66,072,096

66,072,096

25 × 32 × 383 × 599
Abundant Even Composite

66,072,096 factors as 2^5 × 3^2 × 383 × 599. Its 72 positive divisors give a proper-divisor sum of 122,625,504, so this integer is abundant. The Collatz stopping time is 83 steps.

Prime Factor Structure

Factorization String 2^5 × 3^2 × 383 × 599
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 72
Divisor Sum (σ) 188,697,600
Proper Divisor Sum 122,625,504
Digit Sum / Digital Root 36 (Root: 9)
Adjacent Primes #66072073 ← → #66072119

Radix Representation

Decimal 66072096
Binary 11111100000010111000100000 (26 bits)
Octal 0o374027040
Hexadecimal 0x3F02E20

Divisor Catalog (60 of 72)

1 2 3 4 6 8 9 12 16 18 24 32 36 48 72 96 144 288 383 599 766 1,149 1,198 1,532 1,797 2,298 2,396 3,064 3,447 3,594 4,596 4,792 5,391 6,128 6,894 7,188 9,192 9,584 10,782 12,256 13,788 14,376 18,384 19,168 21,564 27,576 28,752 36,768 43,128 55,152 57,504 86,256 110,304 172,512 229,417 458,834 688,251 917,668 1,376,502 1,835,336

Collatz Trajectory (83 steps to reach 1)

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

66,072,096 33,036,048 16,518,024 8,259,012 4,129,506 2,064,753 6,194,260 3,097,130 1,548,565 4,645,696 2,322,848 1,161,424 580,712 290,356 145,178 72,589 217,768 108,884 54,442 27,221 81,664 40,832 20,416 10,208 5,104 2,552 1,276 638 319 958 479 1,438 719 2,158 1,079 3,238 1,619 4,858 2,429 7,288 3,644 1,822 911 2,734 1,367 4,102 2,051 6,154 3,077 9,232 4,616 2,308 1,154 577 1,732 866 433 1,300 650 325

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