729,742

2 × 13² × 17 × 127

Starting at 729,742, the Collatz iteration reaches 1 after 198 steps. The first transition is 364871; the starting value is even with 24 positive divisors.

Prime Factor Structure

Factorization String 2 × 13^2 × 17 × 127

Distinct Prime Factors 4

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 24

Divisor Sum (σ) 1,264,896

Proper Divisor Sum 535,154

Digit Sum / Digital Root 31 (Root: 4)

Adjacent Primes #729737 ← → #729749

Radix Representation

Decimal	729742
Binary	10110010001010001110 (20 bits)
Octal	0o2621216
Hexadecimal	0xB228E

Divisor Catalog (24)

1 2 13 17 26 34 127 169 221 254 338 442 1,651 2,159 2,873 3,302 4,318 5,746 21,463 28,067 42,926 56,134 364,871 729,742

Collatz Trajectory (198 steps to reach 1)

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

729,742 364,871 1,094,614 547,307 1,641,922 820,961 2,462,884 1,231,442 615,721 1,847,164 923,582 461,791 1,385,374 692,687 2,078,062 1,039,031 3,117,094 1,558,547 4,675,642 2,337,821 7,013,464 3,506,732 1,753,366 876,683 2,630,050 1,315,025 3,945,076 1,972,538 986,269 2,958,808 1,479,404 739,702 369,851 1,109,554 554,777 1,664,332 832,166 416,083 1,248,250 624,125 1,872,376 936,188 468,094 234,047 702,142 351,071 1,053,214 526,607 1,579,822 789,911 2,369,734 1,184,867 3,554,602 1,777,301 5,331,904 2,665,952 1,332,976 666,488 333,244 166,622

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