687,591

3² × 19 × 4021

687,591 factors as 3^2 × 19 × 4021. Its 12 positive divisors give a proper-divisor sum of 358,129, so this integer is deficient. The Collatz stopping time is 105 steps.

Prime Factor Structure

Factorization String 3^2 × 19 × 4021

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 12

Divisor Sum (σ) 1,045,720

Proper Divisor Sum 358,129

Digit Sum / Digital Root 36 (Root: 9)

Adjacent Primes #687581 ← → #687593

Radix Representation

Decimal	687591
Binary	10100111110111100111 (20 bits)
Octal	0o2476747
Hexadecimal	0xA7DE7

Divisor Catalog (12)

1 3 9 19 57 171 4,021 12,063 36,189 76,399 229,197 687,591

Collatz Trajectory (105 steps to reach 1)

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

687,591 2,062,774 1,031,387 3,094,162 1,547,081 4,641,244 2,320,622 1,160,311 3,480,934 1,740,467 5,221,402 2,610,701 7,832,104 3,916,052 1,958,026 979,013 2,937,040 1,468,520 734,260 367,130 183,565 550,696 275,348 137,674 68,837 206,512 103,256 51,628 25,814 12,907 38,722 19,361 58,084 29,042 14,521 43,564 21,782 10,891 32,674 16,337 49,012 24,506 12,253 36,760 18,380 9,190 4,595 13,786 6,893 20,680 10,340 5,170 2,585 7,756 3,878 1,939 5,818 2,909 8,728 4,364

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