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Atlas › Integer Profiles › Node 17,529,006

17,529,006

2 × 3 × 11 × 172 × 919
Abundant Even Composite

17,529,006 factors as 2 × 3 × 11 × 17^2 × 919. Its 48 positive divisors give a proper-divisor sum of 23,142,354, so this integer is abundant. The Collatz stopping time is 363 steps.

Prime Factor Structure

Factorization String 2 × 3 × 11 × 17^2 × 919
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 40,671,360
Proper Divisor Sum 23,142,354
Digit Sum / Digital Root 30 (Root: 3)
Adjacent Primes #17528999 ← → #17529007

Radix Representation

Decimal 17529006
Binary 1000010110111100010101110 (25 bits)
Octal 0o102674256
Hexadecimal 0x10B78AE

Divisor Catalog (48)

1 2 3 6 11 17 22 33 34 51 66 102 187 289 374 561 578 867 919 1,122 1,734 1,838 2,757 3,179 5,514 6,358 9,537 10,109 15,623 19,074 20,218 30,327 31,246 46,869 60,654 93,738 171,853 265,591 343,706 515,559 531,182 796,773 1,031,118 1,593,546 2,921,501 5,843,002 8,764,503 17,529,006

Collatz Trajectory (363 steps to reach 1)

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

17,529,006 8,764,503 26,293,510 13,146,755 39,440,266 19,720,133 59,160,400 29,580,200 14,790,100 7,395,050 3,697,525 11,092,576 5,546,288 2,773,144 1,386,572 693,286 346,643 1,039,930 519,965 1,559,896 779,948 389,974 194,987 584,962 292,481 877,444 438,722 219,361 658,084 329,042 164,521 493,564 246,782 123,391 370,174 185,087 555,262 277,631 832,894 416,447 1,249,342 624,671 1,874,014 937,007 2,811,022 1,405,511 4,216,534 2,108,267 6,324,802 3,162,401 9,487,204 4,743,602 2,371,801 7,115,404 3,557,702 1,778,851 5,336,554 2,668,277 8,004,832 4,002,416

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