9,788,616

2³ × 3² × 23² × 257

Starting at 9,788,616, the Collatz iteration reaches 1 after 114 steps. The first transition is 4894308; the starting value is even with 72 positive divisors.

Prime Factor Structure

Factorization String 2^3 × 3^2 × 23^2 × 257

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 72

Divisor Sum (σ) 27,821,430

Proper Divisor Sum 18,032,814

Digit Sum / Digital Root 45 (Root: 9)

Adjacent Primes #9788599 ← → #9788657

Radix Representation

Decimal	9788616
Binary	100101010101110011001000 (24 bits)
Octal	0o45256310
Hexadecimal	0x955CC8

Divisor Catalog (60 of 72)

1 2 3 4 6 8 9 12 18 23 24 36 46 69 72 92 138 184 207 257 276 414 514 529 552 771 828 1,028 1,058 1,542 1,587 1,656 2,056 2,116 2,313 3,084 3,174 4,232 4,626 4,761 5,911 6,168 6,348 9,252 9,522 11,822 12,696 17,733 18,504 19,044 23,644 35,466 38,088 47,288 53,199 70,932 106,398 135,953 141,864 212,796

Collatz Trajectory (114 steps to reach 1)

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

9,788,616 4,894,308 2,447,154 1,223,577 3,670,732 1,835,366 917,683 2,753,050 1,376,525 4,129,576 2,064,788 1,032,394 516,197 1,548,592 774,296 387,148 193,574 96,787 290,362 145,181 435,544 217,772 108,886 54,443 163,330 81,665 244,996 122,498 61,249 183,748 91,874 45,937 137,812 68,906 34,453 103,360 51,680 25,840 12,920 6,460 3,230 1,615 4,846 2,423 7,270 3,635 10,906 5,453 16,360 8,180 4,090 2,045 6,136 3,068 1,534 767 2,302 1,151 3,454 1,727

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