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Atlas › Integer Profiles › Node 13,634,170

13,634,170

2 × 5 × 11 × 17 × 23 × 317
Abundant Even Composite

13,634,170 factors as 2 × 5 × 11 × 17 × 23 × 317. Its 64 positive divisors give a proper-divisor sum of 16,039,046, so this integer is abundant. The Collatz stopping time is 223 steps.

Prime Factor Structure

Factorization String 2 × 5 × 11 × 17 × 23 × 317
Distinct Prime Factors 6
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 64
Divisor Sum (σ) 29,673,216
Proper Divisor Sum 16,039,046
Digit Sum / Digital Root 25 (Root: 7)
Adjacent Primes #13634143 ← → #13634189

Radix Representation

Decimal 13634170
Binary 110100000000101001111010 (24 bits)
Octal 0o64005172
Hexadecimal 0xD00A7A

Divisor Catalog (60 of 64)

1 2 5 10 11 17 22 23 34 46 55 85 110 115 170 187 230 253 317 374 391 506 634 782 935 1,265 1,585 1,870 1,955 2,530 3,170 3,487 3,910 4,301 5,389 6,974 7,291 8,602 10,778 14,582 17,435 21,505 26,945 34,870 36,455 43,010 53,890 59,279 72,910 80,201 118,558 123,947 160,402 247,894 296,395 401,005 592,790 619,735 802,010 1,239,470

Collatz Trajectory (223 steps to reach 1)

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

13,634,170 6,817,085 20,451,256 10,225,628 5,112,814 2,556,407 7,669,222 3,834,611 11,503,834 5,751,917 17,255,752 8,627,876 4,313,938 2,156,969 6,470,908 3,235,454 1,617,727 4,853,182 2,426,591 7,279,774 3,639,887 10,919,662 5,459,831 16,379,494 8,189,747 24,569,242 12,284,621 36,853,864 18,426,932 9,213,466 4,606,733 13,820,200 6,910,100 3,455,050 1,727,525 5,182,576 2,591,288 1,295,644 647,822 323,911 971,734 485,867 1,457,602 728,801 2,186,404 1,093,202 546,601 1,639,804 819,902 409,951 1,229,854 614,927 1,844,782 922,391 2,767,174 1,383,587 4,150,762 2,075,381 6,226,144 3,113,072

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