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Atlas › Integer Profiles › Node 9,701,928

9,701,928

23 × 32 × 472 × 61
Abundant Even Composite

9,701,928 factors as 2^3 × 3^2 × 47^2 × 61. Its 72 positive divisors give a proper-divisor sum of 17,585,202, so this integer is abundant. The Collatz stopping time is 101 steps.

Prime Factor Structure

Factorization String 2^3 × 3^2 × 47^2 × 61
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 72
Divisor Sum (σ) 27,287,130
Proper Divisor Sum 17,585,202
Digit Sum / Digital Root 36 (Root: 9)
Adjacent Primes #9701927 ← → #9701933

Radix Representation

Decimal 9701928
Binary 100101000000101000101000 (24 bits)
Octal 0o45005050
Hexadecimal 0x940A28

Divisor Catalog (60 of 72)

1 2 3 4 6 8 9 12 18 24 36 47 61 72 94 122 141 183 188 244 282 366 376 423 488 549 564 732 846 1,098 1,128 1,464 1,692 2,196 2,209 2,867 3,384 4,392 4,418 5,734 6,627 8,601 8,836 11,468 13,254 17,202 17,672 19,881 22,936 25,803 26,508 34,404 39,762 51,606 53,016 68,808 79,524 103,212 134,749 159,048

Collatz Trajectory (101 steps to reach 1)

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

9,701,928 4,850,964 2,425,482 1,212,741 3,638,224 1,819,112 909,556 454,778 227,389 682,168 341,084 170,542 85,271 255,814 127,907 383,722 191,861 575,584 287,792 143,896 71,948 35,974 17,987 53,962 26,981 80,944 40,472 20,236 10,118 5,059 15,178 7,589 22,768 11,384 5,692 2,846 1,423 4,270 2,135 6,406 3,203 9,610 4,805 14,416 7,208 3,604 1,802 901 2,704 1,352 676 338 169 508 254 127 382 191 574 287

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