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Atlas › Integer Profiles › Node 8,001,812

8,001,812

22 × 7 × 132 × 19 × 89
Abundant Even Composite

8,001,812 factors as 2^2 × 7 × 13^2 × 19 × 89. Its 72 positive divisors give a proper-divisor sum of 10,444,588, so this integer is abundant. The Collatz stopping time is 142 steps.

Prime Factor Structure

Factorization String 2^2 × 7 × 13^2 × 19 × 89
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 72
Divisor Sum (σ) 18,446,400
Proper Divisor Sum 10,444,588
Digit Sum / Digital Root 20 (Root: 2)
Adjacent Primes #8001811 ← → #8001823

Radix Representation

Decimal 8001812
Binary 11110100001100100010100 (23 bits)
Octal 0o36414424
Hexadecimal 0x7A1914

Divisor Catalog (60 of 72)

1 2 4 7 13 14 19 26 28 38 52 76 89 91 133 169 178 182 247 266 338 356 364 494 532 623 676 988 1,157 1,183 1,246 1,691 1,729 2,314 2,366 2,492 3,211 3,382 3,458 4,628 4,732 6,422 6,764 6,916 8,099 11,837 12,844 15,041 16,198 21,983 22,477 23,674 30,082 32,396 43,966 44,954 47,348 60,164 87,932 89,908

Collatz Trajectory (142 steps to reach 1)

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

8,001,812 4,000,906 2,000,453 6,001,360 3,000,680 1,500,340 750,170 375,085 1,125,256 562,628 281,314 140,657 421,972 210,986 105,493 316,480 158,240 79,120 39,560 19,780 9,890 4,945 14,836 7,418 3,709 11,128 5,564 2,782 1,391 4,174 2,087 6,262 3,131 9,394 4,697 14,092 7,046 3,523 10,570 5,285 15,856 7,928 3,964 1,982 991 2,974 1,487 4,462 2,231 6,694 3,347 10,042 5,021 15,064 7,532 3,766 1,883 5,650 2,825 8,476

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