721,782

2 × 3² × 40099

721,782 has digital root 9. The neighboring primes are 721739 and 721783; its proper-divisor sum differs from the starting integer by 120,336.

Prime Factor Structure

Factorization String 2 × 3^2 × 40099

Distinct Prime Factors 3

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 12

Divisor Sum (σ) 1,563,900

Proper Divisor Sum 842,118

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #721739 ← → #721783

Radix Representation

Decimal	721782
Binary	10110000001101110110 (20 bits)
Octal	0o2601566
Hexadecimal	0xB0376

Divisor Catalog (12)

1 2 3 6 9 18 40,099 80,198 120,297 240,594 360,891 721,782

Collatz Trajectory (229 steps to reach 1)

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

721,782 360,891 1,082,674 541,337 1,624,012 812,006 406,003 1,218,010 609,005 1,827,016 913,508 456,754 228,377 685,132 342,566 171,283 513,850 256,925 770,776 385,388 192,694 96,347 289,042 144,521 433,564 216,782 108,391 325,174 162,587 487,762 243,881 731,644 365,822 182,911 548,734 274,367 823,102 411,551 1,234,654 617,327 1,851,982 925,991 2,777,974 1,388,987 4,166,962 2,083,481 6,250,444 3,125,222 1,562,611 4,687,834 2,343,917 7,031,752 3,515,876 1,757,938 878,969 2,636,908 1,318,454 659,227 1,977,682 988,841

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