λ
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Atlas › Integer Profiles › Node 86,367,648

86,367,648

25 × 3 × 41 × 21943
Abundant Even Composite

86,367,648 factors as 2^5 × 3 × 41 × 21943. Its 48 positive divisors give a proper-divisor sum of 145,887,648, so this integer is abundant. The Collatz stopping time is 143 steps.

Prime Factor Structure

Factorization String 2^5 × 3 × 41 × 21943
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 232,255,296
Proper Divisor Sum 145,887,648
Digit Sum / Digital Root 48 (Root: 3)
Adjacent Primes #86367637 ← → #86367653

Radix Representation

Decimal 86367648
Binary 101001001011101110110100000 (27 bits)
Octal 0o511356640
Hexadecimal 0x525DDA0

Divisor Catalog (48)

1 2 3 4 6 8 12 16 24 32 41 48 82 96 123 164 246 328 492 656 984 1,312 1,968 3,936 21,943 43,886 65,829 87,772 131,658 175,544 263,316 351,088 526,632 702,176 899,663 1,053,264 1,799,326 2,106,528 2,698,989 3,598,652 5,397,978 7,197,304 10,795,956 14,394,608 21,591,912 28,789,216 43,183,824 86,367,648

Collatz Trajectory (143 steps to reach 1)

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

86,367,648 43,183,824 21,591,912 10,795,956 5,397,978 2,698,989 8,096,968 4,048,484 2,024,242 1,012,121 3,036,364 1,518,182 759,091 2,277,274 1,138,637 3,415,912 1,707,956 853,978 426,989 1,280,968 640,484 320,242 160,121 480,364 240,182 120,091 360,274 180,137 540,412 270,206 135,103 405,310 202,655 607,966 303,983 911,950 455,975 1,367,926 683,963 2,051,890 1,025,945 3,077,836 1,538,918 769,459 2,308,378 1,154,189 3,462,568 1,731,284 865,642 432,821 1,298,464 649,232 324,616 162,308 81,154 40,577 121,732 60,866 30,433 91,300

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