λ
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Atlas › Integer Profiles › Node 13,640,744

13,640,744

23 × 13 × 31 × 4231
Abundant Even Composite

13,640,744 factors as 2^3 × 13 × 31 × 4231. Its 32 positive divisors give a proper-divisor sum of 14,798,296, so this integer is abundant. The Collatz stopping time is 78 steps.

Prime Factor Structure

Factorization String 2^3 × 13 × 31 × 4231
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 32
Divisor Sum (σ) 28,439,040
Proper Divisor Sum 14,798,296
Digit Sum / Digital Root 29 (Root: 2)
Adjacent Primes #13640743 ← → #13640747

Radix Representation

Decimal 13640744
Binary 110100000010010000101000 (24 bits)
Octal 0o64022050
Hexadecimal 0xD02428

Divisor Catalog (32)

1 2 4 8 13 26 31 52 62 104 124 248 403 806 1,612 3,224 4,231 8,462 16,924 33,848 55,003 110,006 131,161 220,012 262,322 440,024 524,644 1,049,288 1,705,093 3,410,186 6,820,372 13,640,744

Collatz Trajectory (78 steps to reach 1)

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

13,640,744 6,820,372 3,410,186 1,705,093 5,115,280 2,557,640 1,278,820 639,410 319,705 959,116 479,558 239,779 719,338 359,669 1,079,008 539,504 269,752 134,876 67,438 33,719 101,158 50,579 151,738 75,869 227,608 113,804 56,902 28,451 85,354 42,677 128,032 64,016 32,008 16,004 8,002 4,001 12,004 6,002 3,001 9,004 4,502 2,251 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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