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Atlas › Integer Profiles › Node 12,891,732

12,891,732

22 × 3 × 7 × 167 × 919
Abundant Even Composite

12,891,732 factors as 2^2 × 3 × 7 × 167 × 919. Its 48 positive divisors give a proper-divisor sum of 21,729,708, so this integer is abundant. The Collatz stopping time is 117 steps.

Prime Factor Structure

Factorization String 2^2 × 3 × 7 × 167 × 919
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 34,621,440
Proper Divisor Sum 21,729,708
Digit Sum / Digital Root 33 (Root: 6)
Adjacent Primes #12891731 ← → #12891737

Radix Representation

Decimal 12891732
Binary 110001001011011001010100 (24 bits)
Octal 0o61133124
Hexadecimal 0xC4B654

Divisor Catalog (48)

1 2 3 4 6 7 12 14 21 28 42 84 167 334 501 668 919 1,002 1,169 1,838 2,004 2,338 2,757 3,507 3,676 4,676 5,514 6,433 7,014 11,028 12,866 14,028 19,299 25,732 38,598 77,196 153,473 306,946 460,419 613,892 920,838 1,074,311 1,841,676 2,148,622 3,222,933 4,297,244 6,445,866 12,891,732

Collatz Trajectory (117 steps to reach 1)

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

12,891,732 6,445,866 3,222,933 9,668,800 4,834,400 2,417,200 1,208,600 604,300 302,150 151,075 453,226 226,613 679,840 339,920 169,960 84,980 42,490 21,245 63,736 31,868 15,934 7,967 23,902 11,951 35,854 17,927 53,782 26,891 80,674 40,337 121,012 60,506 30,253 90,760 45,380 22,690 11,345 34,036 17,018 8,509 25,528 12,764 6,382 3,191 9,574 4,787 14,362 7,181 21,544 10,772 5,386 2,693 8,080 4,040 2,020 1,010 505 1,516 758 379

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