3,337,929

3⁴ × 7² × 29²

Starting at 3,337,929, the Collatz iteration reaches 1 after 89 steps. The first transition is 10013788; the starting value is odd with 45 positive divisors.

Prime Factor Structure

Factorization String 3^4 × 7^2 × 29^2

Distinct Prime Factors 3

Square Status Yes (√3337929 = 1827)

Abundance Measure Deficient

Analytical Properties

Total Divisors 45

Divisor Sum (σ) 6,007,287

Proper Divisor Sum 2,669,358

Digit Sum / Digital Root 36 (Root: 9)

Adjacent Primes #3337927 ← → #3337931

Radix Representation

Decimal	3337929
Binary	1100101110111011001001 (22 bits)
Octal	0o14567311
Hexadecimal	0x32EEC9

Divisor Catalog (45)

1 3 7 9 21 27 29 49 63 81 87 147 189 203 261 441 567 609 783 841 1,323 1,421 1,827 2,349 2,523 3,969 4,263 5,481 5,887 7,569 12,789 16,443 17,661 22,707 38,367 41,209 52,983 68,121 115,101 123,627 158,949 370,881 476,847 1,112,643 3,337,929

Collatz Trajectory (89 steps to reach 1)

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

3,337,929 10,013,788 5,006,894 2,503,447 7,510,342 3,755,171 11,265,514 5,632,757 16,898,272 8,449,136 4,224,568 2,112,284 1,056,142 528,071 1,584,214 792,107 2,376,322 1,188,161 3,564,484 1,782,242 891,121 2,673,364 1,336,682 668,341 2,005,024 1,002,512 501,256 250,628 125,314 62,657 187,972 93,986 46,993 140,980 70,490 35,245 105,736 52,868 26,434 13,217 39,652 19,826 9,913 29,740 14,870 7,435 22,306 11,153 33,460 16,730 8,365 25,096 12,548 6,274 3,137 9,412 4,706 2,353 7,060 3,530

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