165,522

2 × 3 × 7² × 563

For 165,522, the 24 positive divisors have a total of 385,776. Removing 165,522 leaves 220,254, which gives the abundant classification.

Prime Factor Structure

Factorization String 2 × 3 × 7^2 × 563

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 24

Divisor Sum (σ) 385,776

Proper Divisor Sum 220,254

Digit Sum / Digital Root 21 (Root: 3)

Adjacent Primes #165511 ← → #165523

Radix Representation

Decimal	165522
Binary	101000011010010010 (18 bits)
Octal	0o503222
Hexadecimal	0x28692

Divisor Catalog (24)

1 2 3 6 7 14 21 42 49 98 147 294 563 1,126 1,689 3,378 3,941 7,882 11,823 23,646 27,587 55,174 82,761 165,522

Collatz Trajectory (152 steps to reach 1)

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

165,522 82,761 248,284 124,142 62,071 186,214 93,107 279,322 139,661 418,984 209,492 104,746 52,373 157,120 78,560 39,280 19,640 9,820 4,910 2,455 7,366 3,683 11,050 5,525 16,576 8,288 4,144 2,072 1,036 518 259 778 389 1,168 584 292 146 73 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182

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