82,646

2 × 31² × 43

Starting at 82,646, the Collatz iteration reaches 1 after 120 steps. The first transition is 41323; the starting value is even with 12 positive divisors.

Prime Factor Structure

Factorization String 2 × 31^2 × 43

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 12

Divisor Sum (σ) 131,076

Proper Divisor Sum 48,430

Digit Sum / Digital Root 26 (Root: 8)

Adjacent Primes #82633 ← → #82651

Radix Representation

Decimal	82646
Binary	10100001011010110 (17 bits)
Octal	0o241326
Hexadecimal	0x142D6

Divisor Catalog (12)

1 2 31 43 62 86 961 1,333 1,922 2,666 41,323 82,646

Collatz Trajectory (120 steps to reach 1)

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

82,646 41,323 123,970 61,985 185,956 92,978 46,489 139,468 69,734 34,867 104,602 52,301 156,904 78,452 39,226 19,613 58,840 29,420 14,710 7,355 22,066 11,033 33,100 16,550 8,275 24,826 12,413 37,240 18,620 9,310 4,655 13,966 6,983 20,950 10,475 31,426 15,713 47,140 23,570 11,785 35,356 17,678 8,839 26,518 13,259 39,778 19,889 59,668 29,834 14,917 44,752 22,376 11,188 5,594 2,797 8,392 4,196 2,098 1,049 3,148

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