λ
Harmonic Matrix

182,009

182009
Deficient Odd Prime

182,009 has digital root 2. The neighboring primes are 181997 and 182011; its proper-divisor sum differs from the starting integer by -182,008.

Prime Factor Structure

Factorization String 182009
Distinct Prime Factors 1
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 2
Divisor Sum (σ) 182,010
Proper Divisor Sum 1
Digit Sum / Digital Root 20 (Root: 2)
Adjacent Primes #181997 ← → #182011

Radix Representation

Decimal 182009
Binary 101100011011111001 (18 bits)
Octal 0o543371
Hexadecimal 0x2C6F9

Divisor Catalog (2)

Collatz Trajectory (85 steps to reach 1)

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

182,009 546,028 273,014 136,507 409,522 204,761 614,284 307,142 153,571 460,714 230,357 691,072 345,536 172,768 86,384 43,192 21,596 10,798 5,399 16,198 8,099 24,298 12,149 36,448 18,224 9,112 4,556 2,278 1,139 3,418 1,709 5,128 2,564 1,282 641 1,924 962 481 1,444 722 361 1,084 542 271 814 407 1,222 611 1,834 917 2,752 1,376 688 344 172 86 43 130 65 196

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