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Atlas › Integer Profiles › Node 86,680,240

86,680,240

24 × 5 × 829 × 1307
Abundant Even Composite

86,680,240 factors as 2^4 × 5 × 829 × 1307. Its 40 positive divisors give a proper-divisor sum of 115,248,800, so this integer is abundant. The Collatz stopping time is 236 steps.

Prime Factor Structure

Factorization String 2^4 × 5 × 829 × 1307
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 40
Divisor Sum (σ) 201,929,040
Proper Divisor Sum 115,248,800
Digit Sum / Digital Root 34 (Root: 7)
Adjacent Primes #86680219 ← → #86680249

Radix Representation

Decimal 86680240
Binary 101001010101010001010110000 (27 bits)
Octal 0o512521260
Hexadecimal 0x52AA2B0

Divisor Catalog (40)

1 2 4 5 8 10 16 20 40 80 829 1,307 1,658 2,614 3,316 4,145 5,228 6,535 6,632 8,290 10,456 13,070 13,264 16,580 20,912 26,140 33,160 52,280 66,320 104,560 1,083,503 2,167,006 4,334,012 5,417,515 8,668,024 10,835,030 17,336,048 21,670,060 43,340,120 86,680,240

Collatz Trajectory (236 steps to reach 1)

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

86,680,240 43,340,120 21,670,060 10,835,030 5,417,515 16,252,546 8,126,273 24,378,820 12,189,410 6,094,705 18,284,116 9,142,058 4,571,029 13,713,088 6,856,544 3,428,272 1,714,136 857,068 428,534 214,267 642,802 321,401 964,204 482,102 241,051 723,154 361,577 1,084,732 542,366 271,183 813,550 406,775 1,220,326 610,163 1,830,490 915,245 2,745,736 1,372,868 686,434 343,217 1,029,652 514,826 257,413 772,240 386,120 193,060 96,530 48,265 144,796 72,398 36,199 108,598 54,299 162,898 81,449 244,348 122,174 61,087 183,262 91,631

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