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Atlas › Integer Profiles › Node 12,949,000

12,949,000

23 × 53 × 23 × 563
Abundant Even Composite

12,949,000 factors as 2^3 × 5^3 × 23 × 563. Its 64 positive divisors give a proper-divisor sum of 18,725,240, so this integer is abundant. The Collatz stopping time is 104 steps.

Prime Factor Structure

Factorization String 2^3 × 5^3 × 23 × 563
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 64
Divisor Sum (σ) 31,674,240
Proper Divisor Sum 18,725,240
Digit Sum / Digital Root 25 (Root: 7)
Adjacent Primes #12948973 ← → #12949003

Radix Representation

Decimal 12949000
Binary 110001011001011000001000 (24 bits)
Octal 0o61313010
Hexadecimal 0xC59608

Divisor Catalog (60 of 64)

1 2 4 5 8 10 20 23 25 40 46 50 92 100 115 125 184 200 230 250 460 500 563 575 920 1,000 1,126 1,150 2,252 2,300 2,815 2,875 4,504 4,600 5,630 5,750 11,260 11,500 12,949 14,075 22,520 23,000 25,898 28,150 51,796 56,300 64,745 70,375 103,592 112,600 129,490 140,750 258,980 281,500 323,725 517,960 563,000 647,450 1,294,900 1,618,625

Collatz Trajectory (104 steps to reach 1)

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

12,949,000 6,474,500 3,237,250 1,618,625 4,855,876 2,427,938 1,213,969 3,641,908 1,820,954 910,477 2,731,432 1,365,716 682,858 341,429 1,024,288 512,144 256,072 128,036 64,018 32,009 96,028 48,014 24,007 72,022 36,011 108,034 54,017 162,052 81,026 40,513 121,540 60,770 30,385 91,156 45,578 22,789 68,368 34,184 17,092 8,546 4,273 12,820 6,410 3,205 9,616 4,808 2,404 1,202 601 1,804 902 451 1,354 677 2,032 1,016 508 254 127 382

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