516,664

2³ × 17 × 29 × 131

Starting at 516,664, the Collatz iteration reaches 1 after 195 steps. The first transition is 258332; the starting value is even with 32 positive divisors.

Prime Factor Structure

Factorization String 2^3 × 17 × 29 × 131

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 32

Divisor Sum (σ) 1,069,200

Proper Divisor Sum 552,536

Digit Sum / Digital Root 28 (Root: 1)

Adjacent Primes #516653 ← → #516673

Radix Representation

Decimal	516664
Binary	1111110001000111000 (19 bits)
Octal	0o1761070
Hexadecimal	0x7E238

Divisor Catalog (32)

1 2 4 8 17 29 34 58 68 116 131 136 232 262 493 524 986 1,048 1,972 2,227 3,799 3,944 4,454 7,598 8,908 15,196 17,816 30,392 64,583 129,166 258,332 516,664

Collatz Trajectory (195 steps to reach 1)

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

516,664 258,332 129,166 64,583 193,750 96,875 290,626 145,313 435,940 217,970 108,985 326,956 163,478 81,739 245,218 122,609 367,828 183,914 91,957 275,872 137,936 68,968 34,484 17,242 8,621 25,864 12,932 6,466 3,233 9,700 4,850 2,425 7,276 3,638 1,819 5,458 2,729 8,188 4,094 2,047 6,142 3,071 9,214 4,607 13,822 6,911 20,734 10,367 31,102 15,551 46,654 23,327 69,982 34,991 104,974 52,487 157,462 78,731 236,194 118,097

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