509,607

3² × 7 × 8089

509,607 factors as 3^2 × 7 × 8089. Its 12 positive divisors give a proper-divisor sum of 331,753, so this integer is deficient. The Collatz stopping time is 107 steps.

Prime Factor Structure

Factorization String 3^2 × 7 × 8089

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 12

Divisor Sum (σ) 841,360

Proper Divisor Sum 331,753

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #509603 ← → #509623

Radix Representation

Decimal	509607
Binary	1111100011010100111 (19 bits)
Octal	0o1743247
Hexadecimal	0x7C6A7

Divisor Catalog (12)

1 3 7 9 21 63 8,089 24,267 56,623 72,801 169,869 509,607

Collatz Trajectory (107 steps to reach 1)

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

509,607 1,528,822 764,411 2,293,234 1,146,617 3,439,852 1,719,926 859,963 2,579,890 1,289,945 3,869,836 1,934,918 967,459 2,902,378 1,451,189 4,353,568 2,176,784 1,088,392 544,196 272,098 136,049 408,148 204,074 102,037 306,112 153,056 76,528 38,264 19,132 9,566 4,783 14,350 7,175 21,526 10,763 32,290 16,145 48,436 24,218 12,109 36,328 18,164 9,082 4,541 13,624 6,812 3,406 1,703 5,110 2,555 7,666 3,833 11,500 5,750 2,875 8,626 4,313 12,940 6,470 3,235

More profiles

Browse other published profiles and their separate link collections.

No other profiles in this collection.

← Previous Integer #509,606 Browse Full Index Next Integer #509,608 →