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Atlas › Integer Profiles › Node 27,142,000

27,142,000

24 × 53 × 41 × 331
Abundant Even Composite

Prime Factor Structure

Factorization String 2^4 × 5^3 × 41 × 331
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 80
Divisor Sum (σ) 67,433,184
Proper Divisor Sum 40,291,184
Digit Sum / Digital Root 16 (Root: 7)
Adjacent Primes #27141997 ← → #27142043

Radix Representation

Decimal 27142000
Binary 1100111100010011101110000 (25 bits)
Octal 0o147423560
Hexadecimal 0x19E2770

Divisor Catalog (60 of 80)

1 2 4 5 8 10 16 20 25 40 41 50 80 82 100 125 164 200 205 250 328 331 400 410 500 656 662 820 1,000 1,025 1,324 1,640 1,655 2,000 2,050 2,648 3,280 3,310 4,100 5,125 5,296 6,620 8,200 8,275 10,250 13,240 13,571 16,400 16,550 20,500 26,480 27,142 33,100 41,000 41,375 54,284 66,200 67,855 82,000 82,750

Collatz Trajectory (87 steps to reach 1)

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

27,142,000 13,571,000 6,785,500 3,392,750 1,696,375 5,089,126 2,544,563 7,633,690 3,816,845 11,450,536 5,725,268 2,862,634 1,431,317 4,293,952 2,146,976 1,073,488 536,744 268,372 134,186 67,093 201,280 100,640 50,320 25,160 12,580 6,290 3,145 9,436 4,718 2,359 7,078 3,539 10,618 5,309 15,928 7,964 3,982 1,991 5,974 2,987 8,962 4,481 13,444 6,722 3,361 10,084 5,042 2,521 7,564 3,782 1,891 5,674 2,837 8,512 4,256 2,128 1,064 532 266 133

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