8,506,758

2 × 3 × 13 × 191 × 571

Starting at 8,506,758, the Collatz iteration reaches 1 after 137 steps. The first transition is 4253379; the starting value is even with 32 positive divisors.

Prime Factor Structure

Factorization String 2 × 3 × 13 × 191 × 571

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 32

Divisor Sum (σ) 18,450,432

Proper Divisor Sum 9,943,674

Digit Sum / Digital Root 39 (Root: 3)

Adjacent Primes #8506717 ← → #8506759

Radix Representation

Decimal	8506758
Binary	100000011100110110000110 (24 bits)
Octal	0o40346606
Hexadecimal	0x81CD86

Divisor Catalog (32)

1 2 3 6 13 26 39 78 191 382 571 573 1,142 1,146 1,713 2,483 3,426 4,966 7,423 7,449 14,846 14,898 22,269 44,538 109,061 218,122 327,183 654,366 1,417,793 2,835,586 4,253,379 8,506,758

Collatz Trajectory (137 steps to reach 1)

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

8,506,758 4,253,379 12,760,138 6,380,069 19,140,208 9,570,104 4,785,052 2,392,526 1,196,263 3,588,790 1,794,395 5,383,186 2,691,593 8,074,780 4,037,390 2,018,695 6,056,086 3,028,043 9,084,130 4,542,065 13,626,196 6,813,098 3,406,549 10,219,648 5,109,824 2,554,912 1,277,456 638,728 319,364 159,682 79,841 239,524 119,762 59,881 179,644 89,822 44,911 134,734 67,367 202,102 101,051 303,154 151,577 454,732 227,366 113,683 341,050 170,525 511,576 255,788 127,894 63,947 191,842 95,921 287,764 143,882 71,941 215,824 107,912 53,956

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