λ
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Atlas › Integer Profiles › Node 21,931,720

21,931,720

23 × 5 × 41 × 43 × 311
Abundant Even Composite

21,931,720 factors as 2^3 × 5 × 41 × 43 × 311. Its 64 positive divisors give a proper-divisor sum of 29,960,120, so this integer is abundant. The Collatz stopping time is 247 steps.

Prime Factor Structure

Factorization String 2^3 × 5 × 41 × 43 × 311
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 64
Divisor Sum (σ) 51,891,840
Proper Divisor Sum 29,960,120
Digit Sum / Digital Root 25 (Root: 7)
Adjacent Primes #21931711 ← → #21931727

Radix Representation

Decimal 21931720
Binary 1010011101010011011001000 (25 bits)
Octal 0o123523310
Hexadecimal 0x14EA6C8

Divisor Catalog (60 of 64)

1 2 4 5 8 10 20 40 41 43 82 86 164 172 205 215 311 328 344 410 430 622 820 860 1,244 1,555 1,640 1,720 1,763 2,488 3,110 3,526 6,220 7,052 8,815 12,440 12,751 13,373 14,104 17,630 25,502 26,746 35,260 51,004 53,492 63,755 66,865 70,520 102,008 106,984 127,510 133,730 255,020 267,460 510,040 534,920 548,293 1,096,586 2,193,172 2,741,465

Collatz Trajectory (247 steps to reach 1)

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

21,931,720 10,965,860 5,482,930 2,741,465 8,224,396 4,112,198 2,056,099 6,168,298 3,084,149 9,252,448 4,626,224 2,313,112 1,156,556 578,278 289,139 867,418 433,709 1,301,128 650,564 325,282 162,641 487,924 243,962 121,981 365,944 182,972 91,486 45,743 137,230 68,615 205,846 102,923 308,770 154,385 463,156 231,578 115,789 347,368 173,684 86,842 43,421 130,264 65,132 32,566 16,283 48,850 24,425 73,276 36,638 18,319 54,958 27,479 82,438 41,219 123,658 61,829 185,488 92,744 46,372 23,186

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