7,585,992

2³ × 3² × 105361

Starting at 7,585,992, the Collatz iteration reaches 1 after 103 steps. The first transition is 3792996; the starting value is even with 24 positive divisors.

Prime Factor Structure

Factorization String 2^3 × 3^2 × 105361

Distinct Prime Factors 3

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 24

Divisor Sum (σ) 20,545,590

Proper Divisor Sum 12,959,598

Digit Sum / Digital Root 45 (Root: 9)

Adjacent Primes #7585987 ← → #7586003

Radix Representation

Decimal	7585992
Binary	11100111100000011001000 (23 bits)
Octal	0o34740310
Hexadecimal	0x73C0C8

Divisor Catalog (24)

1 2 3 4 6 8 9 12 18 24 36 72 105,361 210,722 316,083 421,444 632,166 842,888 948,249 1,264,332 1,896,498 2,528,664 3,792,996 7,585,992

Collatz Trajectory (103 steps to reach 1)

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

7,585,992 3,792,996 1,896,498 948,249 2,844,748 1,422,374 711,187 2,133,562 1,066,781 3,200,344 1,600,172 800,086 400,043 1,200,130 600,065 1,800,196 900,098 450,049 1,350,148 675,074 337,537 1,012,612 506,306 253,153 759,460 379,730 189,865 569,596 284,798 142,399 427,198 213,599 640,798 320,399 961,198 480,599 1,441,798 720,899 2,162,698 1,081,349 3,244,048 1,622,024 811,012 405,506 202,753 608,260 304,130 152,065 456,196 228,098 114,049 342,148 171,074 85,537 256,612 128,306 64,153 192,460 96,230 48,115

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