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Atlas › Integer Profiles › Node 8,281,820

8,281,820

22 × 5 × 29 × 109 × 131
Abundant Even Composite

8,281,820 factors as 2^2 × 5 × 29 × 109 × 131. Its 48 positive divisors give a proper-divisor sum of 10,013,380, so this integer is abundant. The Collatz stopping time is 137 steps.

Prime Factor Structure

Factorization String 2^2 × 5 × 29 × 109 × 131
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 18,295,200
Proper Divisor Sum 10,013,380
Digit Sum / Digital Root 29 (Root: 2)
Adjacent Primes #8281813 ← → #8281831

Radix Representation

Decimal 8281820
Binary 11111100101111011011100 (23 bits)
Octal 0o37457334
Hexadecimal 0x7E5EDC

Divisor Catalog (48)

1 2 4 5 10 20 29 58 109 116 131 145 218 262 290 436 524 545 580 655 1,090 1,310 2,180 2,620 3,161 3,799 6,322 7,598 12,644 14,279 15,196 15,805 18,995 28,558 31,610 37,990 57,116 63,220 71,395 75,980 142,790 285,580 414,091 828,182 1,656,364 2,070,455 4,140,910 8,281,820

Collatz Trajectory (137 steps to reach 1)

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

8,281,820 4,140,910 2,070,455 6,211,366 3,105,683 9,317,050 4,658,525 13,975,576 6,987,788 3,493,894 1,746,947 5,240,842 2,620,421 7,861,264 3,930,632 1,965,316 982,658 491,329 1,473,988 736,994 368,497 1,105,492 552,746 276,373 829,120 414,560 207,280 103,640 51,820 25,910 12,955 38,866 19,433 58,300 29,150 14,575 43,726 21,863 65,590 32,795 98,386 49,193 147,580 73,790 36,895 110,686 55,343 166,030 83,015 249,046 124,523 373,570 186,785 560,356 280,178 140,089 420,268 210,134 105,067 315,202

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