6,406,209

3⁵ × 41 × 643

Starting at 6,406,209, the Collatz iteration reaches 1 after 240 steps. The first transition is 19218628; the starting value is odd with 24 positive divisors.

Prime Factor Structure

Factorization String 3^5 × 41 × 643

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 24

Divisor Sum (σ) 9,845,472

Proper Divisor Sum 3,439,263

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #6406199 ← → #6406219

Radix Representation

Decimal	6406209
Binary	11000011100000001000001 (23 bits)
Octal	0o30340101
Hexadecimal	0x61C041

Divisor Catalog (24)

1 3 9 27 41 81 123 243 369 643 1,107 1,929 3,321 5,787 9,963 17,361 26,363 52,083 79,089 156,249 237,267 711,801 2,135,403 6,406,209

Collatz Trajectory (240 steps to reach 1)

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

6,406,209 19,218,628 9,609,314 4,804,657 14,413,972 7,206,986 3,603,493 10,810,480 5,405,240 2,702,620 1,351,310 675,655 2,026,966 1,013,483 3,040,450 1,520,225 4,560,676 2,280,338 1,140,169 3,420,508 1,710,254 855,127 2,565,382 1,282,691 3,848,074 1,924,037 5,772,112 2,886,056 1,443,028 721,514 360,757 1,082,272 541,136 270,568 135,284 67,642 33,821 101,464 50,732 25,366 12,683 38,050 19,025 57,076 28,538 14,269 42,808 21,404 10,702 5,351 16,054 8,027 24,082 12,041 36,124 18,062 9,031 27,094 13,547 40,642

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