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Atlas › Integer Profiles › Node 13,386,760

13,386,760

23 × 5 × 432 × 181
Abundant Even Composite

13,386,760 factors as 2^3 × 5 × 43^2 × 181. Its 48 positive divisors give a proper-divisor sum of 17,620,580, so this integer is abundant. The Collatz stopping time is 135 steps.

Prime Factor Structure

Factorization String 2^3 × 5 × 43^2 × 181
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 31,007,340
Proper Divisor Sum 17,620,580
Digit Sum / Digital Root 34 (Root: 7)
Adjacent Primes #13386733 ← → #13386767

Radix Representation

Decimal 13386760
Binary 110011000100010000001000 (24 bits)
Octal 0o63042010
Hexadecimal 0xCC4408

Divisor Catalog (48)

1 2 4 5 8 10 20 40 43 86 172 181 215 344 362 430 724 860 905 1,448 1,720 1,810 1,849 3,620 3,698 7,240 7,396 7,783 9,245 14,792 15,566 18,490 31,132 36,980 38,915 62,264 73,960 77,830 155,660 311,320 334,669 669,338 1,338,676 1,673,345 2,677,352 3,346,690 6,693,380 13,386,760

Collatz Trajectory (135 steps to reach 1)

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

13,386,760 6,693,380 3,346,690 1,673,345 5,020,036 2,510,018 1,255,009 3,765,028 1,882,514 941,257 2,823,772 1,411,886 705,943 2,117,830 1,058,915 3,176,746 1,588,373 4,765,120 2,382,560 1,191,280 595,640 297,820 148,910 74,455 223,366 111,683 335,050 167,525 502,576 251,288 125,644 62,822 31,411 94,234 47,117 141,352 70,676 35,338 17,669 53,008 26,504 13,252 6,626 3,313 9,940 4,970 2,485 7,456 3,728 1,864 932 466 233 700 350 175 526 263 790 395

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