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Atlas › Integer Profiles › Node 13,645,000

13,645,000

23 × 54 × 2729
Abundant Even Composite

13,645,000 factors as 2^3 × 5^4 × 2729. Its 40 positive divisors give a proper-divisor sum of 18,336,950, so this integer is abundant. The Collatz stopping time is 78 steps.

Prime Factor Structure

Factorization String 2^3 × 5^4 × 2729
Distinct Prime Factors 3
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 40
Divisor Sum (σ) 31,981,950
Proper Divisor Sum 18,336,950
Digit Sum / Digital Root 19 (Root: 1)
Adjacent Primes #13644997 ← → #13645001

Radix Representation

Decimal 13645000
Binary 110100000011010011001000 (24 bits)
Octal 0o64032310
Hexadecimal 0xD034C8

Divisor Catalog (40)

1 2 4 5 8 10 20 25 40 50 100 125 200 250 500 625 1,000 1,250 2,500 2,729 5,000 5,458 10,916 13,645 21,832 27,290 54,580 68,225 109,160 136,450 272,900 341,125 545,800 682,250 1,364,500 1,705,625 2,729,000 3,411,250 6,822,500 13,645,000

Collatz Trajectory (78 steps to reach 1)

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

13,645,000 6,822,500 3,411,250 1,705,625 5,116,876 2,558,438 1,279,219 3,837,658 1,918,829 5,756,488 2,878,244 1,439,122 719,561 2,158,684 1,079,342 539,671 1,619,014 809,507 2,428,522 1,214,261 3,642,784 1,821,392 910,696 455,348 227,674 113,837 341,512 170,756 85,378 42,689 128,068 64,034 32,017 96,052 48,026 24,013 72,040 36,020 18,010 9,005 27,016 13,508 6,754 3,377 10,132 5,066 2,533 7,600 3,800 1,900 950 475 1,426 713 2,140 1,070 535 1,606 803 2,410

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