686,154

2 × 3 × 7 × 17 × 31²

686,154 factors as 2 × 3 × 7 × 17 × 31^2. Its 48 positive divisors give a proper-divisor sum of 1,029,750, so this integer is abundant. The Collatz stopping time is 105 steps.

Prime Factor Structure

Factorization String 2 × 3 × 7 × 17 × 31^2

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 48

Divisor Sum (σ) 1,715,904

Proper Divisor Sum 1,029,750

Digit Sum / Digital Root 30 (Root: 3)

Adjacent Primes #686149 ← → #686173

Radix Representation

Decimal	686154
Binary	10100111100001001010 (20 bits)
Octal	0o2474112
Hexadecimal	0xA784A

Divisor Catalog (48)

1 2 3 6 7 14 17 21 31 34 42 51 62 93 102 119 186 217 238 357 434 527 651 714 961 1,054 1,302 1,581 1,922 2,883 3,162 3,689 5,766 6,727 7,378 11,067 13,454 16,337 20,181 22,134 32,674 40,362 49,011 98,022 114,359 228,718 343,077 686,154

Collatz Trajectory (105 steps to reach 1)

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

686,154 343,077 1,029,232 514,616 257,308 128,654 64,327 192,982 96,491 289,474 144,737 434,212 217,106 108,553 325,660 162,830 81,415 244,246 122,123 366,370 183,185 549,556 274,778 137,389 412,168 206,084 103,042 51,521 154,564 77,282 38,641 115,924 57,962 28,981 86,944 43,472 21,736 10,868 5,434 2,717 8,152 4,076 2,038 1,019 3,058 1,529 4,588 2,294 1,147 3,442 1,721 5,164 2,582 1,291 3,874 1,937 5,812 2,906 1,453 4,360

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