509,616

2⁴ × 3² × 3539

509,616 factors as 2^4 × 3^2 × 3539. Its 30 positive divisors give a proper-divisor sum of 917,004, so this integer is abundant. The Collatz stopping time is 138 steps.

Prime Factor Structure

Factorization String 2^4 × 3^2 × 3539

Distinct Prime Factors 3

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 30

Divisor Sum (σ) 1,426,620

Proper Divisor Sum 917,004

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #509603 ← → #509623

Radix Representation

Decimal	509616
Binary	1111100011010110000 (19 bits)
Octal	0o1743260
Hexadecimal	0x7C6B0

Divisor Catalog (30)

1 2 3 4 6 8 9 12 16 18 24 36 48 72 144 3,539 7,078 10,617 14,156 21,234 28,312 31,851 42,468 56,624 63,702 84,936 127,404 169,872 254,808 509,616

Collatz Trajectory (138 steps to reach 1)

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

509,616 254,808 127,404 63,702 31,851 95,554 47,777 143,332 71,666 35,833 107,500 53,750 26,875 80,626 40,313 120,940 60,470 30,235 90,706 45,353 136,060 68,030 34,015 102,046 51,023 153,070 76,535 229,606 114,803 344,410 172,205 516,616 258,308 129,154 64,577 193,732 96,866 48,433 145,300 72,650 36,325 108,976 54,488 27,244 13,622 6,811 20,434 10,217 30,652 15,326 7,663 22,990 11,495 34,486 17,243 51,730 25,865 77,596 38,798 19,399

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