805,653

3³ × 53 × 563

Starting at 805,653, the Collatz iteration reaches 1 after 113 steps. The first transition is 2416960; the starting value is odd with 16 positive divisors.

Prime Factor Structure

Factorization String 3^3 × 53 × 563

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 16

Divisor Sum (σ) 1,218,240

Proper Divisor Sum 412,587

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #805639 ← → #805687

Radix Representation

Decimal	805653
Binary	11000100101100010101 (20 bits)
Octal	0o3045425
Hexadecimal	0xC4B15

Divisor Catalog (16)

1 3 9 27 53 159 477 563 1,431 1,689 5,067 15,201 29,839 89,517 268,551 805,653

Collatz Trajectory (113 steps to reach 1)

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

805,653 2,416,960 1,208,480 604,240 302,120 151,060 75,530 37,765 113,296 56,648 28,324 14,162 7,081 21,244 10,622 5,311 15,934 7,967 23,902 11,951 35,854 17,927 53,782 26,891 80,674 40,337 121,012 60,506 30,253 90,760 45,380 22,690 11,345 34,036 17,018 8,509 25,528 12,764 6,382 3,191 9,574 4,787 14,362 7,181 21,544 10,772 5,386 2,693 8,080 4,040 2,020 1,010 505 1,516 758 379 1,138 569 1,708 854

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