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Atlas › Integer Profiles › Node 17,564,000

17,564,000

25 × 53 × 4391
Abundant Even Composite

17,564,000 factors as 2^5 × 5^3 × 4391. Its 48 positive divisors give a proper-divisor sum of 25,600,576, so this integer is abundant. The Collatz stopping time is 138 steps.

Prime Factor Structure

Factorization String 2^5 × 5^3 × 4391
Distinct Prime Factors 3
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 43,164,576
Proper Divisor Sum 25,600,576
Digit Sum / Digital Root 23 (Root: 5)
Adjacent Primes #17563993 ← → #17564021

Radix Representation

Decimal 17564000
Binary 1000011000000000101100000 (25 bits)
Octal 0o103000540
Hexadecimal 0x10C0160

Divisor Catalog (48)

1 2 4 5 8 10 16 20 25 32 40 50 80 100 125 160 200 250 400 500 800 1,000 2,000 4,000 4,391 8,782 17,564 21,955 35,128 43,910 70,256 87,820 109,775 140,512 175,640 219,550 351,280 439,100 548,875 702,560 878,200 1,097,750 1,756,400 2,195,500 3,512,800 4,391,000 8,782,000 17,564,000

Collatz Trajectory (138 steps to reach 1)

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

17,564,000 8,782,000 4,391,000 2,195,500 1,097,750 548,875 1,646,626 823,313 2,469,940 1,234,970 617,485 1,852,456 926,228 463,114 231,557 694,672 347,336 173,668 86,834 43,417 130,252 65,126 32,563 97,690 48,845 146,536 73,268 36,634 18,317 54,952 27,476 13,738 6,869 20,608 10,304 5,152 2,576 1,288 644 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526

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