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Atlas › Integer Profiles › Node 429,840

429,840

24 × 33 × 5 × 199
Abundant Even Composite

Prime Factor Structure

Factorization String 2^4 × 3^3 × 5 × 199
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 80
Divisor Sum (σ) 1,488,000
Proper Divisor Sum 1,058,160
Digit Sum / Digital Root 27 (Root: 9)
Adjacent Primes #429827 ← → #429851

Radix Representation

Decimal 429840
Binary 1101000111100010000 (19 bits)
Octal 0o1507420
Hexadecimal 0x68F10

Divisor Catalog (60 of 80)

1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 27 30 36 40 45 48 54 60 72 80 90 108 120 135 144 180 199 216 240 270 360 398 432 540 597 720 796 995 1,080 1,194 1,592 1,791 1,990 2,160 2,388 2,985 3,184 3,582 3,980 4,776 5,373 5,970 7,164 7,960 8,955

Collatz Trajectory (94 steps to reach 1)

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

429,840 214,920 107,460 53,730 26,865 80,596 40,298 20,149 60,448 30,224 15,112 7,556 3,778 1,889 5,668 2,834 1,417 4,252 2,126 1,063 3,190 1,595 4,786 2,393 7,180 3,590 1,795 5,386 2,693 8,080 4,040 2,020 1,010 505 1,516 758 379 1,138 569 1,708 854 427 1,282 641 1,924 962 481 1,444 722 361 1,084 542 271 814 407 1,222 611 1,834 917 2,752

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