309,387

3 × 13 × 7933

Starting at 309,387, the Collatz iteration reaches 1 after 83 steps. The first transition is 928162; the starting value is odd with 8 positive divisors.

Prime Factor Structure

Factorization String 3 × 13 × 7933

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 8

Divisor Sum (σ) 444,304

Proper Divisor Sum 134,917

Digit Sum / Digital Root 30 (Root: 3)

Adjacent Primes #309371 ← → #309391

Radix Representation

Decimal	309387
Binary	1001011100010001011 (19 bits)
Octal	0o1134213
Hexadecimal	0x4B88B

Divisor Catalog (8)

1 3 13 39 7,933 23,799 103,129 309,387

Collatz Trajectory (83 steps to reach 1)

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

309,387 928,162 464,081 1,392,244 696,122 348,061 1,044,184 522,092 261,046 130,523 391,570 195,785 587,356 293,678 146,839 440,518 220,259 660,778 330,389 991,168 495,584 247,792 123,896 61,948 30,974 15,487 46,462 23,231 69,694 34,847 104,542 52,271 156,814 78,407 235,222 117,611 352,834 176,417 529,252 264,626 132,313 396,940 198,470 99,235 297,706 148,853 446,560 223,280 111,640 55,820 27,910 13,955 41,866 20,933 62,800 31,400 15,700 7,850 3,925 11,776

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