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Atlas › Integer Profiles › Node 9,505,664

9,505,664

27 × 7 × 1032
Abundant Even Composite

9,505,664 factors as 2^7 × 7 × 103^2. Its 48 positive divisors give a proper-divisor sum of 12,348,856, so this integer is abundant. The Collatz stopping time is 75 steps.

Prime Factor Structure

Factorization String 2^7 × 7 × 103^2
Distinct Prime Factors 3
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 21,854,520
Proper Divisor Sum 12,348,856
Digit Sum / Digital Root 35 (Root: 8)
Adjacent Primes #9505663 ← → #9505679

Radix Representation

Decimal 9505664
Binary 100100010000101110000000 (24 bits)
Octal 0o44205600
Hexadecimal 0x910B80

Divisor Catalog (48)

1 2 4 7 8 14 16 28 32 56 64 103 112 128 206 224 412 448 721 824 896 1,442 1,648 2,884 3,296 5,768 6,592 10,609 11,536 13,184 21,218 23,072 42,436 46,144 74,263 84,872 92,288 148,526 169,744 297,052 339,488 594,104 678,976 1,188,208 1,357,952 2,376,416 4,752,832 9,505,664

Collatz Trajectory (75 steps to reach 1)

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

9,505,664 4,752,832 2,376,416 1,188,208 594,104 297,052 148,526 74,263 222,790 111,395 334,186 167,093 501,280 250,640 125,320 62,660 31,330 15,665 46,996 23,498 11,749 35,248 17,624 8,812 4,406 2,203 6,610 3,305 9,916 4,958 2,479 7,438 3,719 11,158 5,579 16,738 8,369 25,108 12,554 6,277 18,832 9,416 4,708 2,354 1,177 3,532 1,766 883 2,650 1,325 3,976 1,988 994 497 1,492 746 373 1,120 560 280

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