8,405,586

2 × 3³ × 7 × 37 × 601

Starting at 8,405,586, the Collatz iteration reaches 1 after 129 steps. The first transition is 4202793; the starting value is even with 64 positive divisors.

Prime Factor Structure

Factorization String 2 × 3^3 × 7 × 37 × 601

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 64

Divisor Sum (σ) 21,960,960

Proper Divisor Sum 13,555,374

Digit Sum / Digital Root 36 (Root: 9)

Adjacent Primes #8405567 ← → #8405587

Radix Representation

Decimal	8405586
Binary	100000000100001001010010 (24 bits)
Octal	0o40041122
Hexadecimal	0x804252

Divisor Catalog (60 of 64)

1 2 3 6 7 9 14 18 21 27 37 42 54 63 74 111 126 189 222 259 333 378 518 601 666 777 999 1,202 1,554 1,803 1,998 2,331 3,606 4,207 4,662 5,409 6,993 8,414 10,818 12,621 13,986 16,227 22,237 25,242 32,454 37,863 44,474 66,711 75,726 113,589 133,422 155,659 200,133 227,178 311,318 400,266 466,977 600,399 933,954 1,200,798

Collatz Trajectory (129 steps to reach 1)

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

8,405,586 4,202,793 12,608,380 6,304,190 3,152,095 9,456,286 4,728,143 14,184,430 7,092,215 21,276,646 10,638,323 31,914,970 15,957,485 47,872,456 23,936,228 11,968,114 5,984,057 17,952,172 8,976,086 4,488,043 13,464,130 6,732,065 20,196,196 10,098,098 5,049,049 15,147,148 7,573,574 3,786,787 11,360,362 5,680,181 17,040,544 8,520,272 4,260,136 2,130,068 1,065,034 532,517 1,597,552 798,776 399,388 199,694 99,847 299,542 149,771 449,314 224,657 673,972 336,986 168,493 505,480 252,740 126,370 63,185 189,556 94,778 47,389 142,168 71,084 35,542 17,771 53,314

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