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Atlas › Integer Profiles › Node 8,213,616

8,213,616

24 × 33 × 19013
Abundant Even Composite

8,213,616 factors as 2^4 × 3^3 × 19013. Its 40 positive divisors give a proper-divisor sum of 15,363,744, so this integer is abundant. The Collatz stopping time is 243 steps.

Prime Factor Structure

Factorization String 2^4 × 3^3 × 19013
Distinct Prime Factors 3
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 40
Divisor Sum (σ) 23,577,360
Proper Divisor Sum 15,363,744
Digit Sum / Digital Root 27 (Root: 9)
Adjacent Primes #8213603 ← → #8213627

Radix Representation

Decimal 8213616
Binary 11111010101010001110000 (23 bits)
Octal 0o37252160
Hexadecimal 0x7D5470

Divisor Catalog (40)

1 2 3 4 6 8 9 12 16 18 24 27 36 48 54 72 108 144 216 432 19,013 38,026 57,039 76,052 114,078 152,104 171,117 228,156 304,208 342,234 456,312 513,351 684,468 912,624 1,026,702 1,368,936 2,053,404 2,737,872 4,106,808 8,213,616

Collatz Trajectory (243 steps to reach 1)

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

8,213,616 4,106,808 2,053,404 1,026,702 513,351 1,540,054 770,027 2,310,082 1,155,041 3,465,124 1,732,562 866,281 2,598,844 1,299,422 649,711 1,949,134 974,567 2,923,702 1,461,851 4,385,554 2,192,777 6,578,332 3,289,166 1,644,583 4,933,750 2,466,875 7,400,626 3,700,313 11,100,940 5,550,470 2,775,235 8,325,706 4,162,853 12,488,560 6,244,280 3,122,140 1,561,070 780,535 2,341,606 1,170,803 3,512,410 1,756,205 5,268,616 2,634,308 1,317,154 658,577 1,975,732 987,866 493,933 1,481,800 740,900 370,450 185,225 555,676 277,838 138,919 416,758 208,379 625,138 312,569

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