208,593

3² × 7² × 11 × 43

208,593 factors as 3^2 × 7^2 × 11 × 43. Its 36 positive divisors give a proper-divisor sum of 182,655, so this integer is deficient. The Collatz stopping time is 80 steps.

Prime Factor Structure

Factorization String 3^2 × 7^2 × 11 × 43

Distinct Prime Factors 4

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 36

Divisor Sum (σ) 391,248

Proper Divisor Sum 182,655

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #208591 ← → #208609

Radix Representation

Decimal	208593
Binary	110010111011010001 (18 bits)
Octal	0o627321
Hexadecimal	0x32ED1

Divisor Catalog (36)

1 3 7 9 11 21 33 43 49 63 77 99 129 147 231 301 387 441 473 539 693 903 1,419 1,617 2,107 2,709 3,311 4,257 4,851 6,321 9,933 18,963 23,177 29,799 69,531 208,593

Collatz Trajectory (80 steps to reach 1)

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

208,593 625,780 312,890 156,445 469,336 234,668 117,334 58,667 176,002 88,001 264,004 132,002 66,001 198,004 99,002 49,501 148,504 74,252 37,126 18,563 55,690 27,845 83,536 41,768 20,884 10,442 5,221 15,664 7,832 3,916 1,958 979 2,938 1,469 4,408 2,204 1,102 551 1,654 827 2,482 1,241 3,724 1,862 931 2,794 1,397 4,192 2,096 1,048 524 262 131 394 197 592 296 148 74 37

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