517,582

2 × 13 × 17 × 1171

Starting at 517,582, the Collatz iteration reaches 1 after 107 steps. The first transition is 258791; the starting value is even with 16 positive divisors.

Prime Factor Structure

Factorization String 2 × 13 × 17 × 1171

Distinct Prime Factors 4

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 16

Divisor Sum (σ) 886,032

Proper Divisor Sum 368,450

Digit Sum / Digital Root 28 (Root: 1)

Adjacent Primes #517577 ← → #517589

Radix Representation

Decimal	517582
Binary	1111110010111001110 (19 bits)
Octal	0o1762716
Hexadecimal	0x7E5CE

Divisor Catalog (16)

1 2 13 17 26 34 221 442 1,171 2,342 15,223 19,907 30,446 39,814 258,791 517,582

Collatz Trajectory (107 steps to reach 1)

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

517,582 258,791 776,374 388,187 1,164,562 582,281 1,746,844 873,422 436,711 1,310,134 655,067 1,965,202 982,601 2,947,804 1,473,902 736,951 2,210,854 1,105,427 3,316,282 1,658,141 4,974,424 2,487,212 1,243,606 621,803 1,865,410 932,705 2,798,116 1,399,058 699,529 2,098,588 1,049,294 524,647 1,573,942 786,971 2,360,914 1,180,457 3,541,372 1,770,686 885,343 2,656,030 1,328,015 3,984,046 1,992,023 5,976,070 2,988,035 8,964,106 4,482,053 13,446,160 6,723,080 3,361,540 1,680,770 840,385 2,521,156 1,260,578 630,289 1,890,868 945,434 472,717 1,418,152 709,076

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