6,417,560

2³ × 5 × 83 × 1933

Starting at 6,417,560, the Collatz iteration reaches 1 after 147 steps. The first transition is 3208780; the starting value is even with 32 positive divisors.

Prime Factor Structure

Factorization String 2^3 × 5 × 83 × 1933

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 32

Divisor Sum (σ) 14,621,040

Proper Divisor Sum 8,203,480

Digit Sum / Digital Root 29 (Root: 2)

Adjacent Primes #6417553 ← → #6417563

Radix Representation

Decimal	6417560
Binary	11000011110110010011000 (23 bits)
Octal	0o30366230
Hexadecimal	0x61EC98

Divisor Catalog (32)

1 2 4 5 8 10 20 40 83 166 332 415 664 830 1,660 1,933 3,320 3,866 7,732 9,665 15,464 19,330 38,660 77,320 160,439 320,878 641,756 802,195 1,283,512 1,604,390 3,208,780 6,417,560

Collatz Trajectory (147 steps to reach 1)

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

6,417,560 3,208,780 1,604,390 802,195 2,406,586 1,203,293 3,609,880 1,804,940 902,470 451,235 1,353,706 676,853 2,030,560 1,015,280 507,640 253,820 126,910 63,455 190,366 95,183 285,550 142,775 428,326 214,163 642,490 321,245 963,736 481,868 240,934 120,467 361,402 180,701 542,104 271,052 135,526 67,763 203,290 101,645 304,936 152,468 76,234 38,117 114,352 57,176 28,588 14,294 7,147 21,442 10,721 32,164 16,082 8,041 24,124 12,062 6,031 18,094 9,047 27,142 13,571 40,714

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