λ
Ratio Atlas
Atlas › Integer Profiles › Node 13,640,520

13,640,520

23 × 3 × 5 × 71 × 1601
Abundant Even Composite

13,640,520 factors as 2^3 × 3 × 5 × 71 × 1601. Its 64 positive divisors give a proper-divisor sum of 27,883,320, so this integer is abundant. The Collatz stopping time is 135 steps.

Prime Factor Structure

Factorization String 2^3 × 3 × 5 × 71 × 1601
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 64
Divisor Sum (σ) 41,523,840
Proper Divisor Sum 27,883,320
Digit Sum / Digital Root 21 (Root: 3)
Adjacent Primes #13640513 ← → #13640521

Radix Representation

Decimal 13640520
Binary 110100000010001101001000 (24 bits)
Octal 0o64021510
Hexadecimal 0xD02348

Divisor Catalog (60 of 64)

1 2 3 4 5 6 8 10 12 15 20 24 30 40 60 71 120 142 213 284 355 426 568 710 852 1,065 1,420 1,601 1,704 2,130 2,840 3,202 4,260 4,803 6,404 8,005 8,520 9,606 12,808 16,010 19,212 24,015 32,020 38,424 48,030 64,040 96,060 113,671 192,120 227,342 341,013 454,684 568,355 682,026 909,368 1,136,710 1,364,052 1,705,065 2,273,420 2,728,104

Collatz Trajectory (135 steps to reach 1)

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

13,640,520 6,820,260 3,410,130 1,705,065 5,115,196 2,557,598 1,278,799 3,836,398 1,918,199 5,754,598 2,877,299 8,631,898 4,315,949 12,947,848 6,473,924 3,236,962 1,618,481 4,855,444 2,427,722 1,213,861 3,641,584 1,820,792 910,396 455,198 227,599 682,798 341,399 1,024,198 512,099 1,536,298 768,149 2,304,448 1,152,224 576,112 288,056 144,028 72,014 36,007 108,022 54,011 162,034 81,017 243,052 121,526 60,763 182,290 91,145 273,436 136,718 68,359 205,078 102,539 307,618 153,809 461,428 230,714 115,357 346,072 173,036 86,518

More profiles

Browse other published profiles and their separate link collections.

No other profiles in this collection.

← Previous Integer #13,640,519 Browse Full Index Next Integer #13,640,521 →