3,687,424

2¹⁰ × 13 × 277

Starting at 3,687,424, the Collatz iteration reaches 1 after 128 steps. The first transition is 1843712; the starting value is even with 44 positive divisors.

Prime Factor Structure

Factorization String 2^10 × 13 × 277

Distinct Prime Factors 3

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 44

Divisor Sum (σ) 7,966,924

Proper Divisor Sum 4,279,500

Digit Sum / Digital Root 34 (Root: 7)

Adjacent Primes #3687421 ← → #3687427

Radix Representation

Decimal	3687424
Binary	1110000100010000000000 (22 bits)
Octal	0o16042000
Hexadecimal	0x384400

Divisor Catalog (44)

1 2 4 8 13 16 26 32 52 64 104 128 208 256 277 416 512 554 832 1,024 1,108 1,664 2,216 3,328 3,601 4,432 6,656 7,202 8,864 13,312 14,404 17,728 28,808 35,456 57,616 70,912 115,232 141,824 230,464 283,648 460,928 921,856 1,843,712 3,687,424

Collatz Trajectory (128 steps to reach 1)

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

3,687,424 1,843,712 921,856 460,928 230,464 115,232 57,616 28,808 14,404 7,202 3,601 10,804 5,402 2,701 8,104 4,052 2,026 1,013 3,040 1,520 760 380 190 95 286 143 430 215 646 323 970 485 1,456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1,186 593 1,780 890 445 1,336 668

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