8,202,627

3⁴ × 101267

Starting at 8,202,627, the Collatz iteration reaches 1 after 106 steps. The first transition is 24607882; the starting value is odd with 10 positive divisors.

Prime Factor Structure

Factorization String 3^4 × 101267

Distinct Prime Factors 2

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 10

Divisor Sum (σ) 12,253,428

Proper Divisor Sum 4,050,801

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #8202613 ← → #8202629

Radix Representation

Decimal	8202627
Binary	11111010010100110000011 (23 bits)
Octal	0o37224603
Hexadecimal	0x7D2983

Divisor Catalog (10)

1 3 9 27 81 101,267 303,801 911,403 2,734,209 8,202,627

Collatz Trajectory (106 steps to reach 1)

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

8,202,627 24,607,882 12,303,941 36,911,824 18,455,912 9,227,956 4,613,978 2,306,989 6,920,968 3,460,484 1,730,242 865,121 2,595,364 1,297,682 648,841 1,946,524 973,262 486,631 1,459,894 729,947 2,189,842 1,094,921 3,284,764 1,642,382 821,191 2,463,574 1,231,787 3,695,362 1,847,681 5,543,044 2,771,522 1,385,761 4,157,284 2,078,642 1,039,321 3,117,964 1,558,982 779,491 2,338,474 1,169,237 3,507,712 1,753,856 876,928 438,464 219,232 109,616 54,808 27,404 13,702 6,851 20,554 10,277 30,832 15,416 7,708 3,854 1,927 5,782 2,891 8,674

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