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Atlas › Integer Profiles › Node 13,206,116

13,206,116

22 × 7 × 11 × 53 × 809
Abundant Even Composite

13,206,116 factors as 2^2 × 7 × 11 × 53 × 809. Its 48 positive divisors give a proper-divisor sum of 16,187,164, so this integer is abundant. The Collatz stopping time is 210 steps.

Prime Factor Structure

Factorization String 2^2 × 7 × 11 × 53 × 809
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 29,393,280
Proper Divisor Sum 16,187,164
Digit Sum / Digital Root 20 (Root: 2)
Adjacent Primes #13206043 ← → #13206131

Radix Representation

Decimal 13206116
Binary 110010011000001001100100 (24 bits)
Octal 0o62301144
Hexadecimal 0xC98264

Divisor Catalog (48)

1 2 4 7 11 14 22 28 44 53 77 106 154 212 308 371 583 742 809 1,166 1,484 1,618 2,332 3,236 4,081 5,663 8,162 8,899 11,326 16,324 17,798 22,652 35,596 42,877 62,293 85,754 124,586 171,508 249,172 300,139 471,647 600,278 943,294 1,200,556 1,886,588 3,301,529 6,603,058 13,206,116

Collatz Trajectory (210 steps to reach 1)

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

13,206,116 6,603,058 3,301,529 9,904,588 4,952,294 2,476,147 7,428,442 3,714,221 11,142,664 5,571,332 2,785,666 1,392,833 4,178,500 2,089,250 1,044,625 3,133,876 1,566,938 783,469 2,350,408 1,175,204 587,602 293,801 881,404 440,702 220,351 661,054 330,527 991,582 495,791 1,487,374 743,687 2,231,062 1,115,531 3,346,594 1,673,297 5,019,892 2,509,946 1,254,973 3,764,920 1,882,460 941,230 470,615 1,411,846 705,923 2,117,770 1,058,885 3,176,656 1,588,328 794,164 397,082 198,541 595,624 297,812 148,906 74,453 223,360 111,680 55,840 27,920 13,960

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