655,899

3 × 19 × 37 × 311

Starting at 655,899, the Collatz iteration reaches 1 after 110 steps. The first transition is 1967698; the starting value is odd with 16 positive divisors.

Prime Factor Structure

Factorization String 3 × 19 × 37 × 311

Distinct Prime Factors 4

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 16

Divisor Sum (σ) 948,480

Proper Divisor Sum 292,581

Digit Sum / Digital Root 42 (Root: 6)

Adjacent Primes #655883 ← → #655901

Radix Representation

Decimal	655899
Binary	10100000001000011011 (20 bits)
Octal	0o2401033
Hexadecimal	0xA021B

Divisor Catalog (16)

1 3 19 37 57 111 311 703 933 2,109 5,909 11,507 17,727 34,521 218,633 655,899

Collatz Trajectory (110 steps to reach 1)

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

655,899 1,967,698 983,849 2,951,548 1,475,774 737,887 2,213,662 1,106,831 3,320,494 1,660,247 4,980,742 2,490,371 7,471,114 3,735,557 11,206,672 5,603,336 2,801,668 1,400,834 700,417 2,101,252 1,050,626 525,313 1,575,940 787,970 393,985 1,181,956 590,978 295,489 886,468 443,234 221,617 664,852 332,426 166,213 498,640 249,320 124,660 62,330 31,165 93,496 46,748 23,374 11,687 35,062 17,531 52,594 26,297 78,892 39,446 19,723 59,170 29,585 88,756 44,378 22,189 66,568 33,284 16,642 8,321 24,964

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