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Atlas › Integer Profiles › Node 65,821,840

65,821,840

24 × 5 × 7 × 117539
Abundant Even Composite

65,821,840 factors as 2^4 × 5 × 7 × 117539. Its 40 positive divisors give a proper-divisor sum of 109,077,680, so this integer is abundant. The Collatz stopping time is 109 steps.

Prime Factor Structure

Factorization String 2^4 × 5 × 7 × 117539
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 40
Divisor Sum (σ) 174,899,520
Proper Divisor Sum 109,077,680
Digit Sum / Digital Root 34 (Root: 7)
Adjacent Primes #65821783 ← → #65821849

Radix Representation

Decimal 65821840
Binary 11111011000101110010010000 (26 bits)
Octal 0o373056220
Hexadecimal 0x3EC5C90

Divisor Catalog (40)

1 2 4 5 7 8 10 14 16 20 28 35 40 56 70 80 112 140 280 560 117,539 235,078 470,156 587,695 822,773 940,312 1,175,390 1,645,546 1,880,624 2,350,780 3,291,092 4,113,865 4,701,560 6,582,184 8,227,730 9,403,120 13,164,368 16,455,460 32,910,920 65,821,840

Collatz Trajectory (109 steps to reach 1)

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

65,821,840 32,910,920 16,455,460 8,227,730 4,113,865 12,341,596 6,170,798 3,085,399 9,256,198 4,628,099 13,884,298 6,942,149 20,826,448 10,413,224 5,206,612 2,603,306 1,301,653 3,904,960 1,952,480 976,240 488,120 244,060 122,030 61,015 183,046 91,523 274,570 137,285 411,856 205,928 102,964 51,482 25,741 77,224 38,612 19,306 9,653 28,960 14,480 7,240 3,620 1,810 905 2,716 1,358 679 2,038 1,019 3,058 1,529 4,588 2,294 1,147 3,442 1,721 5,164 2,582 1,291 3,874 1,937

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