λ
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Atlas › Integer Profiles › Node 9,739,752

9,739,752

23 × 3 × 11 × 79 × 467
Abundant Even Composite

9,739,752 factors as 2^3 × 3 × 11 × 79 × 467. Its 64 positive divisors give a proper-divisor sum of 17,217,048, so this integer is abundant. The Collatz stopping time is 238 steps.

Prime Factor Structure

Factorization String 2^3 × 3 × 11 × 79 × 467
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 64
Divisor Sum (σ) 26,956,800
Proper Divisor Sum 17,217,048
Digit Sum / Digital Root 42 (Root: 6)
Adjacent Primes #9739747 ← → #9739771

Radix Representation

Decimal 9739752
Binary 100101001001110111101000 (24 bits)
Octal 0o45116750
Hexadecimal 0x949DE8

Divisor Catalog (60 of 64)

1 2 3 4 6 8 11 12 22 24 33 44 66 79 88 132 158 237 264 316 467 474 632 869 934 948 1,401 1,738 1,868 1,896 2,607 2,802 3,476 3,736 5,137 5,214 5,604 6,952 10,274 10,428 11,208 15,411 20,548 20,856 30,822 36,893 41,096 61,644 73,786 110,679 123,288 147,572 221,358 295,144 405,823 442,716 811,646 885,432 1,217,469 1,623,292

Collatz Trajectory (238 steps to reach 1)

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

9,739,752 4,869,876 2,434,938 1,217,469 3,652,408 1,826,204 913,102 456,551 1,369,654 684,827 2,054,482 1,027,241 3,081,724 1,540,862 770,431 2,311,294 1,155,647 3,466,942 1,733,471 5,200,414 2,600,207 7,800,622 3,900,311 11,700,934 5,850,467 17,551,402 8,775,701 26,327,104 13,163,552 6,581,776 3,290,888 1,645,444 822,722 411,361 1,234,084 617,042 308,521 925,564 462,782 231,391 694,174 347,087 1,041,262 520,631 1,561,894 780,947 2,342,842 1,171,421 3,514,264 1,757,132 878,566 439,283 1,317,850 658,925 1,976,776 988,388 494,194 247,097 741,292 370,646

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