9,729,132

2² × 3 × 7 × 115823

9,729,132 factors as 2^2 × 3 × 7 × 115823. Its 24 positive divisors give a proper-divisor sum of 16,215,444, so this integer is abundant. The Collatz stopping time is 199 steps.

Prime Factor Structure

Factorization String 2^2 × 3 × 7 × 115823

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 24

Divisor Sum (σ) 25,944,576

Proper Divisor Sum 16,215,444

Digit Sum / Digital Root 33 (Root: 6)

Adjacent Primes #9729131 ← → #9729143

Radix Representation

Decimal	9729132
Binary	100101000111010001101100 (24 bits)
Octal	0o45072154
Hexadecimal	0x94746C

Divisor Catalog (24)

1 2 3 4 6 7 12 14 21 28 42 84 115,823 231,646 347,469 463,292 694,938 810,761 1,389,876 1,621,522 2,432,283 3,243,044 4,864,566 9,729,132

Collatz Trajectory (199 steps to reach 1)

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

9,729,132 4,864,566 2,432,283 7,296,850 3,648,425 10,945,276 5,472,638 2,736,319 8,208,958 4,104,479 12,313,438 6,156,719 18,470,158 9,235,079 27,705,238 13,852,619 41,557,858 20,778,929 62,336,788 31,168,394 15,584,197 46,752,592 23,376,296 11,688,148 5,844,074 2,922,037 8,766,112 4,383,056 2,191,528 1,095,764 547,882 273,941 821,824 410,912 205,456 102,728 51,364 25,682 12,841 38,524 19,262 9,631 28,894 14,447 43,342 21,671 65,014 32,507 97,522 48,761 146,284 73,142 36,571 109,714 54,857 164,572 82,286 41,143 123,430 61,715

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