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Atlas › Integer Profiles › Node 9,852,780

9,852,780

22 × 3 × 5 × 7 × 23459
Abundant Even Composite

9,852,780 factors as 2^2 × 3 × 5 × 7 × 23459. Its 48 positive divisors give a proper-divisor sum of 21,677,460, so this integer is abundant. The Collatz stopping time is 83 steps.

Prime Factor Structure

Factorization String 2^2 × 3 × 5 × 7 × 23459
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 31,530,240
Proper Divisor Sum 21,677,460
Digit Sum / Digital Root 39 (Root: 3)
Adjacent Primes #9852743 ← → #9852827

Radix Representation

Decimal 9852780
Binary 100101100101011101101100 (24 bits)
Octal 0o45453554
Hexadecimal 0x96576C

Divisor Catalog (48)

1 2 3 4 5 6 7 10 12 14 15 20 21 28 30 35 42 60 70 84 105 140 210 420 23,459 46,918 70,377 93,836 117,295 140,754 164,213 234,590 281,508 328,426 351,885 469,180 492,639 656,852 703,770 821,065 985,278 1,407,540 1,642,130 1,970,556 2,463,195 3,284,260 4,926,390 9,852,780

Collatz Trajectory (83 steps to reach 1)

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

9,852,780 4,926,390 2,463,195 7,389,586 3,694,793 11,084,380 5,542,190 2,771,095 8,313,286 4,156,643 12,469,930 6,234,965 18,704,896 9,352,448 4,676,224 2,338,112 1,169,056 584,528 292,264 146,132 73,066 36,533 109,600 54,800 27,400 13,700 6,850 3,425 10,276 5,138 2,569 7,708 3,854 1,927 5,782 2,891 8,674 4,337 13,012 6,506 3,253 9,760 4,880 2,440 1,220 610 305 916 458 229 688 344 172 86 43 130 65 196 98 49

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