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Atlas › Integer Profiles › Node 13,800,400

13,800,400

24 × 52 × 34501
Abundant Even Composite

13,800,400 factors as 2^4 × 5^2 × 34501. Its 30 positive divisors give a proper-divisor sum of 19,356,022, so this integer is abundant. The Collatz stopping time is 99 steps.

Prime Factor Structure

Factorization String 2^4 × 5^2 × 34501
Distinct Prime Factors 3
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 30
Divisor Sum (σ) 33,156,422
Proper Divisor Sum 19,356,022
Digit Sum / Digital Root 16 (Root: 7)
Adjacent Primes #13800389 ← → #13800443

Radix Representation

Decimal 13800400
Binary 110100101001001111010000 (24 bits)
Octal 0o64511720
Hexadecimal 0xD293D0

Divisor Catalog (30)

1 2 4 5 8 10 16 20 25 40 50 80 100 200 400 34,501 69,002 138,004 172,505 276,008 345,010 552,016 690,020 862,525 1,380,040 1,725,050 2,760,080 3,450,100 6,900,200 13,800,400

Collatz Trajectory (99 steps to reach 1)

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

13,800,400 6,900,200 3,450,100 1,725,050 862,525 2,587,576 1,293,788 646,894 323,447 970,342 485,171 1,455,514 727,757 2,183,272 1,091,636 545,818 272,909 818,728 409,364 204,682 102,341 307,024 153,512 76,756 38,378 19,189 57,568 28,784 14,392 7,196 3,598 1,799 5,398 2,699 8,098 4,049 12,148 6,074 3,037 9,112 4,556 2,278 1,139 3,418 1,709 5,128 2,564 1,282 641 1,924 962 481 1,444 722 361 1,084 542 271 814 407

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