164,844

2² × 3² × 19 × 241

Starting at 164,844, the Collatz iteration reaches 1 after 214 steps. The first transition is 82422; the starting value is even with 36 positive divisors.

Prime Factor Structure

Factorization String 2^2 × 3^2 × 19 × 241

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 36

Divisor Sum (σ) 440,440

Proper Divisor Sum 275,596

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #164839 ← → #164881

Radix Representation

Decimal	164844
Binary	101000001111101100 (18 bits)
Octal	0o501754
Hexadecimal	0x283EC

Divisor Catalog (36)

1 2 3 4 6 9 12 18 19 36 38 57 76 114 171 228 241 342 482 684 723 964 1,446 2,169 2,892 4,338 4,579 8,676 9,158 13,737 18,316 27,474 41,211 54,948 82,422 164,844

Collatz Trajectory (214 steps to reach 1)

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

164,844 82,422 41,211 123,634 61,817 185,452 92,726 46,363 139,090 69,545 208,636 104,318 52,159 156,478 78,239 234,718 117,359 352,078 176,039 528,118 264,059 792,178 396,089 1,188,268 594,134 297,067 891,202 445,601 1,336,804 668,402 334,201 1,002,604 501,302 250,651 751,954 375,977 1,127,932 563,966 281,983 845,950 422,975 1,268,926 634,463 1,903,390 951,695 2,855,086 1,427,543 4,282,630 2,141,315 6,423,946 3,211,973 9,635,920 4,817,960 2,408,980 1,204,490 602,245 1,806,736 903,368 451,684 225,842

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