λ
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Atlas › Integer Profiles › Node 9,729,705

9,729,705

3 × 5 × 37 × 47 × 373
Deficient Odd Composite

9,729,705 factors as 3 × 5 × 37 × 47 × 373. Its 32 positive divisors give a proper-divisor sum of 6,642,519, so this integer is deficient. The Collatz stopping time is 344 steps.

Prime Factor Structure

Factorization String 3 × 5 × 37 × 47 × 373
Distinct Prime Factors 5
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 32
Divisor Sum (σ) 16,372,224
Proper Divisor Sum 6,642,519
Digit Sum / Digital Root 39 (Root: 3)
Adjacent Primes #9729697 ← → #9729743

Radix Representation

Decimal 9729705
Binary 100101000111011010101001 (24 bits)
Octal 0o45073251
Hexadecimal 0x9476A9

Divisor Catalog (32)

1 3 5 15 37 47 111 141 185 235 373 555 705 1,119 1,739 1,865 5,217 5,595 8,695 13,801 17,531 26,085 41,403 52,593 69,005 87,655 207,015 262,965 648,647 1,945,941 3,243,235 9,729,705

Collatz Trajectory (344 steps to reach 1)

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

9,729,705 29,189,116 14,594,558 7,297,279 21,891,838 10,945,919 32,837,758 16,418,879 49,256,638 24,628,319 73,884,958 36,942,479 110,827,438 55,413,719 166,241,158 83,120,579 249,361,738 124,680,869 374,042,608 187,021,304 93,510,652 46,755,326 23,377,663 70,132,990 35,066,495 105,199,486 52,599,743 157,799,230 78,899,615 236,698,846 118,349,423 355,048,270 177,524,135 532,572,406 266,286,203 798,858,610 399,429,305 1,198,287,916 599,143,958 299,571,979 898,715,938 449,357,969 1,348,073,908 674,036,954 337,018,477 1,011,055,432 505,527,716 252,763,858 126,381,929 379,145,788 189,572,894 94,786,447 284,359,342 142,179,671 426,539,014 213,269,507 639,808,522 319,904,261 959,712,784 479,856,392

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