208,065

3 × 5 × 11 × 13 × 97

208,065 has digital root 3. The neighboring primes are 208057 and 208067; its proper-divisor sum differs from the starting integer by -20,994.

Prime Factor Structure

Factorization String 3 × 5 × 11 × 13 × 97

Distinct Prime Factors 5

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 32

Divisor Sum (σ) 395,136

Proper Divisor Sum 187,071

Digit Sum / Digital Root 21 (Root: 3)

Adjacent Primes #208057 ← → #208067

Radix Representation

Decimal	208065
Binary	110010110011000001 (18 bits)
Octal	0o626301
Hexadecimal	0x32CC1

Divisor Catalog (32)

1 3 5 11 13 15 33 39 55 65 97 143 165 195 291 429 485 715 1,067 1,261 1,455 2,145 3,201 3,783 5,335 6,305 13,871 16,005 18,915 41,613 69,355 208,065

Collatz Trajectory (129 steps to reach 1)

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

208,065 624,196 312,098 156,049 468,148 234,074 117,037 351,112 175,556 87,778 43,889 131,668 65,834 32,917 98,752 49,376 24,688 12,344 6,172 3,086 1,543 4,630 2,315 6,946 3,473 10,420 5,210 2,605 7,816 3,908 1,954 977 2,932 1,466 733 2,200 1,100 550 275 826 413 1,240 620 310 155 466 233 700 350 175 526 263 790 395 1,186 593 1,780 890 445 1,336

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