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Atlas › Integer Profiles › Node 12,923,960

12,923,960

23 × 5 × 7 × 101 × 457
Abundant Even Composite

12,923,960 factors as 2^3 × 5 × 7 × 101 × 457. Its 64 positive divisors give a proper-divisor sum of 20,711,560, so this integer is abundant. The Collatz stopping time is 210 steps.

Prime Factor Structure

Factorization String 2^3 × 5 × 7 × 101 × 457
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 64
Divisor Sum (σ) 33,635,520
Proper Divisor Sum 20,711,560
Digit Sum / Digital Root 32 (Root: 5)
Adjacent Primes #12923947 ← → #12923983

Radix Representation

Decimal 12923960
Binary 110001010011010000111000 (24 bits)
Octal 0o61232070
Hexadecimal 0xC53438

Divisor Catalog (60 of 64)

1 2 4 5 7 8 10 14 20 28 35 40 56 70 101 140 202 280 404 457 505 707 808 914 1,010 1,414 1,828 2,020 2,285 2,828 3,199 3,535 3,656 4,040 4,570 5,656 6,398 7,070 9,140 12,796 14,140 15,995 18,280 25,592 28,280 31,990 46,157 63,980 92,314 127,960 184,628 230,785 323,099 369,256 461,570 646,198 923,140 1,292,396 1,615,495 1,846,280

Collatz Trajectory (210 steps to reach 1)

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

12,923,960 6,461,980 3,230,990 1,615,495 4,846,486 2,423,243 7,269,730 3,634,865 10,904,596 5,452,298 2,726,149 8,178,448 4,089,224 2,044,612 1,022,306 511,153 1,533,460 766,730 383,365 1,150,096 575,048 287,524 143,762 71,881 215,644 107,822 53,911 161,734 80,867 242,602 121,301 363,904 181,952 90,976 45,488 22,744 11,372 5,686 2,843 8,530 4,265 12,796 6,398 3,199 9,598 4,799 14,398 7,199 21,598 10,799 32,398 16,199 48,598 24,299 72,898 36,449 109,348 54,674 27,337 82,012

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