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Atlas › Integer Profiles › Node 80,916,408

80,916,408

23 × 34 × 193 × 647
Abundant Even Composite

80,916,408 factors as 2^3 × 3^4 × 193 × 647. Its 80 positive divisors give a proper-divisor sum of 147,250,872, so this integer is abundant. The Collatz stopping time is 135 steps.

Prime Factor Structure

Factorization String 2^3 × 3^4 × 193 × 647
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 80
Divisor Sum (σ) 228,167,280
Proper Divisor Sum 147,250,872
Digit Sum / Digital Root 36 (Root: 9)
Adjacent Primes #80916403 ← → #80916427

Radix Representation

Decimal 80916408
Binary 100110100101010111110111000 (27 bits)
Octal 0o464527670
Hexadecimal 0x4D2AFB8

Divisor Catalog (60 of 80)

1 2 3 4 6 8 9 12 18 24 27 36 54 72 81 108 162 193 216 324 386 579 647 648 772 1,158 1,294 1,544 1,737 1,941 2,316 2,588 3,474 3,882 4,632 5,176 5,211 5,823 6,948 7,764 10,422 11,646 13,896 15,528 15,633 17,469 20,844 23,292 31,266 34,938 41,688 46,584 52,407 62,532 69,876 104,814 124,871 125,064 139,752 209,628

Collatz Trajectory (135 steps to reach 1)

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

80,916,408 40,458,204 20,229,102 10,114,551 30,343,654 15,171,827 45,515,482 22,757,741 68,273,224 34,136,612 17,068,306 8,534,153 25,602,460 12,801,230 6,400,615 19,201,846 9,600,923 28,802,770 14,401,385 43,204,156 21,602,078 10,801,039 32,403,118 16,201,559 48,604,678 24,302,339 72,907,018 36,453,509 109,360,528 54,680,264 27,340,132 13,670,066 6,835,033 20,505,100 10,252,550 5,126,275 15,378,826 7,689,413 23,068,240 11,534,120 5,767,060 2,883,530 1,441,765 4,325,296 2,162,648 1,081,324 540,662 270,331 810,994 405,497 1,216,492 608,246 304,123 912,370 456,185 1,368,556 684,278 342,139 1,026,418 513,209

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