λ
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Atlas › Integer Profiles › Node 80,964,135

80,964,135

32 × 5 × 7 × 41 × 6269
Abundant Odd Composite

80,964,135 factors as 3^2 × 5 × 7 × 41 × 6269. Its 48 positive divisors give a proper-divisor sum of 83,360,025, so this integer is abundant. The Collatz stopping time is 135 steps.

Prime Factor Structure

Factorization String 3^2 × 5 × 7 × 41 × 6269
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 164,324,160
Proper Divisor Sum 83,360,025
Digit Sum / Digital Root 36 (Root: 9)
Adjacent Primes #80964133 ← → #80964139

Radix Representation

Decimal 80964135
Binary 100110100110110101000100111 (27 bits)
Octal 0o464665047
Hexadecimal 0x4D36A27

Divisor Catalog (48)

1 3 5 7 9 15 21 35 41 45 63 105 123 205 287 315 369 615 861 1,435 1,845 2,583 4,305 6,269 12,915 18,807 31,345 43,883 56,421 94,035 131,649 219,415 257,029 282,105 394,947 658,245 771,087 1,285,145 1,799,203 1,974,735 2,313,261 3,855,435 5,397,609 8,996,015 11,566,305 16,192,827 26,988,045 80,964,135

Collatz Trajectory (135 steps to reach 1)

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

80,964,135 242,892,406 121,446,203 364,338,610 182,169,305 546,507,916 273,253,958 136,626,979 409,880,938 204,940,469 614,821,408 307,410,704 153,705,352 76,852,676 38,426,338 19,213,169 57,639,508 28,819,754 14,409,877 43,229,632 21,614,816 10,807,408 5,403,704 2,701,852 1,350,926 675,463 2,026,390 1,013,195 3,039,586 1,519,793 4,559,380 2,279,690 1,139,845 3,419,536 1,709,768 854,884 427,442 213,721 641,164 320,582 160,291 480,874 240,437 721,312 360,656 180,328 90,164 45,082 22,541 67,624 33,812 16,906 8,453 25,360 12,680 6,340 3,170 1,585 4,756 2,378

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