520,002

2 × 3² × 7 × 4127

520,002 factors as 2 × 3^2 × 7 × 4127. Its 24 positive divisors give a proper-divisor sum of 767,934, so this integer is abundant. The Collatz stopping time is 102 steps.

Prime Factor Structure

Factorization String 2 × 3^2 × 7 × 4127

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 24

Divisor Sum (σ) 1,287,936

Proper Divisor Sum 767,934

Digit Sum / Digital Root 9 (Root: 9)

Adjacent Primes #519997 ← → #520019

Radix Representation

Decimal	520002
Binary	1111110111101000010 (19 bits)
Octal	0o1767502
Hexadecimal	0x7EF42

Divisor Catalog (24)

1 2 3 6 7 9 14 18 21 42 63 126 4,127 8,254 12,381 24,762 28,889 37,143 57,778 74,286 86,667 173,334 260,001 520,002

Collatz Trajectory (102 steps to reach 1)

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

520,002 260,001 780,004 390,002 195,001 585,004 292,502 146,251 438,754 219,377 658,132 329,066 164,533 493,600 246,800 123,400 61,700 30,850 15,425 46,276 23,138 11,569 34,708 17,354 8,677 26,032 13,016 6,508 3,254 1,627 4,882 2,441 7,324 3,662 1,831 5,494 2,747 8,242 4,121 12,364 6,182 3,091 9,274 4,637 13,912 6,956 3,478 1,739 5,218 2,609 7,828 3,914 1,957 5,872 2,936 1,468 734 367 1,102 551

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