506,319

3 × 11 × 67 × 229

506,319 factors as 3 × 11 × 67 × 229. Its 16 positive divisors give a proper-divisor sum of 244,401, so this integer is deficient. The Collatz stopping time is 133 steps.

Prime Factor Structure

Factorization String 3 × 11 × 67 × 229

Distinct Prime Factors 4

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 16

Divisor Sum (σ) 750,720

Proper Divisor Sum 244,401

Digit Sum / Digital Root 24 (Root: 6)

Adjacent Primes #506291 ← → #506327

Radix Representation

Decimal	506319
Binary	1111011100111001111 (19 bits)
Octal	0o1734717
Hexadecimal	0x7B9CF

Divisor Catalog (16)

1 3 11 33 67 201 229 687 737 2,211 2,519 7,557 15,343 46,029 168,773 506,319

Collatz Trajectory (133 steps to reach 1)

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

506,319 1,518,958 759,479 2,278,438 1,139,219 3,417,658 1,708,829 5,126,488 2,563,244 1,281,622 640,811 1,922,434 961,217 2,883,652 1,441,826 720,913 2,162,740 1,081,370 540,685 1,622,056 811,028 405,514 202,757 608,272 304,136 152,068 76,034 38,017 114,052 57,026 28,513 85,540 42,770 21,385 64,156 32,078 16,039 48,118 24,059 72,178 36,089 108,268 54,134 27,067 81,202 40,601 121,804 60,902 30,451 91,354 45,677 137,032 68,516 34,258 17,129 51,388 25,694 12,847 38,542 19,271

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