820,166

2 × 127 × 3229

Starting at 820,166, the Collatz iteration reaches 1 after 175 steps. The first transition is 410083; the starting value is even with 8 positive divisors.

Prime Factor Structure

Factorization String 2 × 127 × 3229

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 8

Divisor Sum (σ) 1,240,320

Proper Divisor Sum 420,154

Digit Sum / Digital Root 23 (Root: 5)

Adjacent Primes #820163 ← → #820177

Radix Representation

Decimal	820166
Binary	11001000001111000110 (20 bits)
Octal	0o3101706
Hexadecimal	0xC83C6

Divisor Catalog (8)

1 2 127 254 3,229 6,458 410,083 820,166

Collatz Trajectory (175 steps to reach 1)

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

820,166 410,083 1,230,250 615,125 1,845,376 922,688 461,344 230,672 115,336 57,668 28,834 14,417 43,252 21,626 10,813 32,440 16,220 8,110 4,055 12,166 6,083 18,250 9,125 27,376 13,688 6,844 3,422 1,711 5,134 2,567 7,702 3,851 11,554 5,777 17,332 8,666 4,333 13,000 6,500 3,250 1,625 4,876 2,438 1,219 3,658 1,829 5,488 2,744 1,372 686 343 1,030 515 1,546 773 2,320 1,160 580 290 145

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