9,852,315

3 × 5 × 11 × 29² × 71

Starting at 9,852,315, the Collatz iteration reaches 1 after 313 steps. The first transition is 29556946; the starting value is odd with 48 positive divisors.

Prime Factor Structure

Factorization String 3 × 5 × 11 × 29^2 × 71

Distinct Prime Factors 5

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 48

Divisor Sum (σ) 18,061,056

Proper Divisor Sum 8,208,741

Digit Sum / Digital Root 33 (Root: 6)

Adjacent Primes #9852313 ← → #9852331

Radix Representation

Decimal	9852315
Binary	100101100101010110011011 (24 bits)
Octal	0o45452633
Hexadecimal	0x96559B

Divisor Catalog (48)

1 3 5 11 15 29 33 55 71 87 145 165 213 319 355 435 781 841 957 1,065 1,595 2,059 2,343 2,523 3,905 4,205 4,785 6,177 9,251 10,295 11,715 12,615 22,649 27,753 30,885 46,255 59,711 67,947 113,245 138,765 179,133 298,555 339,735 656,821 895,665 1,970,463 3,284,105 9,852,315

Collatz Trajectory (313 steps to reach 1)

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

9,852,315 29,556,946 14,778,473 44,335,420 22,167,710 11,083,855 33,251,566 16,625,783 49,877,350 24,938,675 74,816,026 37,408,013 112,224,040 56,112,020 28,056,010 14,028,005 42,084,016 21,042,008 10,521,004 5,260,502 2,630,251 7,890,754 3,945,377 11,836,132 5,918,066 2,959,033 8,877,100 4,438,550 2,219,275 6,657,826 3,328,913 9,986,740 4,993,370 2,496,685 7,490,056 3,745,028 1,872,514 936,257 2,808,772 1,404,386 702,193 2,106,580 1,053,290 526,645 1,579,936 789,968 394,984 197,492 98,746 49,373 148,120 74,060 37,030 18,515 55,546 27,773 83,320 41,660 20,830 10,415

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