516,504

2³ × 3 × 21521

516,504 factors as 2^3 × 3 × 21521. Its 16 positive divisors give a proper-divisor sum of 774,816, so this integer is abundant. The Collatz stopping time is 195 steps.

Prime Factor Structure

Factorization String 2^3 × 3 × 21521

Distinct Prime Factors 3

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 16

Divisor Sum (σ) 1,291,320

Proper Divisor Sum 774,816

Digit Sum / Digital Root 21 (Root: 3)

Adjacent Primes #516499 ← → #516517

Radix Representation

Decimal	516504
Binary	1111110000110011000 (19 bits)
Octal	0o1760630
Hexadecimal	0x7E198

Divisor Catalog (16)

1 2 3 4 6 8 12 24 21,521 43,042 64,563 86,084 129,126 172,168 258,252 516,504

Collatz Trajectory (195 steps to reach 1)

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

516,504 258,252 129,126 64,563 193,690 96,845 290,536 145,268 72,634 36,317 108,952 54,476 27,238 13,619 40,858 20,429 61,288 30,644 15,322 7,661 22,984 11,492 5,746 2,873 8,620 4,310 2,155 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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