85,626

2 × 3² × 67 × 71

Starting at 85,626, the Collatz iteration reaches 1 after 195 steps. The first transition is 42813; the starting value is even with 24 positive divisors.

Prime Factor Structure

Factorization String 2 × 3^2 × 67 × 71

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 24

Divisor Sum (σ) 190,944

Proper Divisor Sum 105,318

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #85621 ← → #85627

Radix Representation

Decimal	85626
Binary	10100111001111010 (17 bits)
Octal	0o247172
Hexadecimal	0x14E7A

Divisor Catalog (24)

1 2 3 6 9 18 67 71 134 142 201 213 402 426 603 639 1,206 1,278 4,757 9,514 14,271 28,542 42,813 85,626

Collatz Trajectory (195 steps to reach 1)

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

85,626 42,813 128,440 64,220 32,110 16,055 48,166 24,083 72,250 36,125 108,376 54,188 27,094 13,547 40,642 20,321 60,964 30,482 15,241 45,724 22,862 11,431 34,294 17,147 51,442 25,721 77,164 38,582 19,291 57,874 28,937 86,812 43,406 21,703 65,110 32,555 97,666 48,833 146,500 73,250 36,625 109,876 54,938 27,469 82,408 41,204 20,602 10,301 30,904 15,452 7,726 3,863 11,590 5,795 17,386 8,693 26,080 13,040 6,520 3,260

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