351,585

3² × 5 × 13 × 601

Starting at 351,585, the Collatz iteration reaches 1 after 272 steps. The first transition is 1054756; the starting value is odd with 24 positive divisors.

Prime Factor Structure

Factorization String 3^2 × 5 × 13 × 601

Distinct Prime Factors 4

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 24

Divisor Sum (σ) 657,384

Proper Divisor Sum 305,799

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #351563 ← → #351587

Radix Representation

Decimal	351585
Binary	1010101110101100001 (19 bits)
Octal	0o1256541
Hexadecimal	0x55D61

Divisor Catalog (24)

1 3 5 9 13 15 39 45 65 117 195 585 601 1,803 3,005 5,409 7,813 9,015 23,439 27,045 39,065 70,317 117,195 351,585

Collatz Trajectory (272 steps to reach 1)

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

351,585 1,054,756 527,378 263,689 791,068 395,534 197,767 593,302 296,651 889,954 444,977 1,334,932 667,466 333,733 1,001,200 500,600 250,300 125,150 62,575 187,726 93,863 281,590 140,795 422,386 211,193 633,580 316,790 158,395 475,186 237,593 712,780 356,390 178,195 534,586 267,293 801,880 400,940 200,470 100,235 300,706 150,353 451,060 225,530 112,765 338,296 169,148 84,574 42,287 126,862 63,431 190,294 95,147 285,442 142,721 428,164 214,082 107,041 321,124 160,562 80,281

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