686,465

5 × 13 × 59 × 179

Starting at 686,465, the Collatz iteration reaches 1 after 105 steps. The first transition is 2059396; the starting value is odd with 16 positive divisors.

Prime Factor Structure

Factorization String 5 × 13 × 59 × 179

Distinct Prime Factors 4

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 16

Divisor Sum (σ) 907,200

Proper Divisor Sum 220,735

Digit Sum / Digital Root 35 (Root: 8)

Adjacent Primes #686453 ← → #686473

Radix Representation

Decimal	686465
Binary	10100111100110000001 (20 bits)
Octal	0o2474601
Hexadecimal	0xA7981

Divisor Catalog (16)

1 5 13 59 65 179 295 767 895 2,327 3,835 10,561 11,635 52,805 137,293 686,465

Collatz Trajectory (105 steps to reach 1)

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

686,465 2,059,396 1,029,698 514,849 1,544,548 772,274 386,137 1,158,412 579,206 289,603 868,810 434,405 1,303,216 651,608 325,804 162,902 81,451 244,354 122,177 366,532 183,266 91,633 274,900 137,450 68,725 206,176 103,088 51,544 25,772 12,886 6,443 19,330 9,665 28,996 14,498 7,249 21,748 10,874 5,437 16,312 8,156 4,078 2,039 6,118 3,059 9,178 4,589 13,768 6,884 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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